3Motion in a Straight Line

📚
MOTION IN A STRAIGHT LINE
▢ Definition:
❖ Rectilinear Motion: Straight-line motion

Table 1: Condition for Straight Line Motion

Condition
Path
Velocity constant
Straight line
Acceleration and velocity at 0°
Straight line
Acceleration and velocity at 180°
Straight line
▢ Distance and Displacement:

Table 1: Distance vs Displacement

Feature
Distance
Displacement
Definition
Length of actual path followed by moving body
Shortest distance between initial and final position with direction
Quantity
Scalar
Vector
Value
Never negative
Positive, negative or zero
For moving body
Always increases with time
May increase or decrease with time
Relation
\(Distance \geq |Displacement|\)
\(|Displacement| \leq Distance\)
▢ Speed and Velocity:

Table 1: Speed vs Velocity

Feature
Speed
Velocity
Definition
Time rate of change of distance
Time rate of change of displacement
Quantity
Scalar
Vector
Formula
\(Speed = \frac{Distance}{Time}\)
\(Velocity = \frac{Displacement}{Time}\)
Value
Never negative
Positive, negative or zero
Types
Uniform, non-uniform, average, instantaneous
Average, instantaneous
❖ Uniform and Non-uniform Speed:

Table 1: Types of Speed

Type
Meaning
Uniform speed
Equal distances in equal time intervals
Non-uniform / variable speed
Equal distances in unequal times OR unequal distances in equal times
❖ Average and Instantaneous Speed:

Table 1: Speed Formulae

Type
Formula
Defined for
Average speed
\(v_{av}=\frac{Total\ distance}{Total\ time}=\frac{x-x_0}{t-t_0}=\frac{\Delta x}{\Delta t}\)
Period of time
Instantaneous speed
\(v_i=\lim_{\Delta t\to0}\frac{\Delta x}{\Delta t}=\frac{dx}{dt}\)
Point of time
❖ Average and Instantaneous Velocity:

Table 1: Velocity Formulae

Type
Formula
Defined for
Average velocity
\(\vec v_{av}=\frac{Total\ displacement}{Total\ time}=\frac{\vec s-\vec s_0}{t-t_0}=\frac{\Delta \vec s}{\Delta t}\)
Period of time
Instantaneous velocity
\(\vec v_i=\lim_{\Delta t\to0}\frac{\Delta \vec s}{\Delta t}=\frac{d\vec s}{dt}\)
Point of time
❖ Average Velocity for Different Segments:
◉ General: \(v_{av}=\frac{s_1+s_2+s_3+...+s_n}{t_1+t_2+t_3+...+t_n}\)
◉ Using Velocities: \(v_{av}=\frac{s_1+s_2+s_3+...+s_n}{\frac{s_1}{v_1}+\frac{s_2}{v_2}+\frac{s_3}{v_3}+...+\frac{s_n}{v_n}}\)
◉ Equal Displacements:
◈ Condition: \(s_1=s_2=s_3=...=s_n\)
◈ Formula: \(\frac{n}{v_{av}}=\frac{1}{v_1}+\frac{1}{v_2}+\frac{1}{v_3}+...+\frac{1}{v_n}\)
◈ Meaning: Average velocity = Harmonic mean
◈ For Two Velocities: \(v_{av}=\frac{2v_1v_2}{v_1+v_2}\)
◉ Equal Times:
◈ Condition: \(t_1=t_2=t_3=...=t_n\)
◈ Formula: \(v_{av}=\frac{v_1+v_2+v_3+...+v_n}{n}\)
◈ Meaning: Average velocity = Arithmetic mean
◈ For Two Velocities: \(v_{av}=\frac{v_1+v_2}{2}\)
◉ Notes:
  • •
    If \(s\) are distances → formula gives average speed
  • •
    If net displacement = 0 → average velocity = 0
▢ Acceleration:
❖ Definition: Time rate of change of velocity
❖ Quantity: Vector

Table 1: Acceleration Types

Type
Formula / Meaning
Average acceleration
\(\vec a_{av}=\frac{\vec v-\vec v_0}{t-t_0}=\frac{\Delta \vec v}{\Delta t}\)
Instantaneous acceleration
\(\vec a_i=\lim_{\Delta t\to0}\frac{\Delta \vec v}{\Delta t}=\frac{d\vec v}{dt}\)
Uniform acceleration
Velocity changes equally in equal time intervals
Variable acceleration
Velocity changes unequally in equal time intervals
▢ Rest and Motion:

Table 1: Motion Based on Displacement-Time Relation

Condition
Relation
Formula / Point
Rest
\(s\propto t^0\)
Position constant
Uniform motion
\(s\propto t\)
\(s=ut\)
Constant acceleration
\(s\propto t^2\)
Equations of motion apply
Variable acceleration
\(s\propto t^3\)
Non-uniform acceleration
▢ Equations of Motion:
❖ Notations:

Table 1: Symbols

Symbol
Meaning
\(s\)
Displacement
\(s_{nth}\)
Displacement in particular second
\(u\)
Initial velocity
\(v\)
Final velocity
\(t\)
Time
\(a\)
Acceleration
❖ Fundamental Formulae:
  • •
    \(v=u+at\)
  • •
    \(v^2=u^2+2as\)
  • •
    \(s=ut+\frac{1}{2}at^2\)
  • •
    \(s_{nth}=u+\frac{a}{2}(2n-1)\)
❖ Generalizations from Rest:

Table 1: Uniform Acceleration from Rest

Quantity
Ratio
Distance up to ends of successive equal time intervals
\(1:4:9:...:n^2\)
Distance in successive equal time intervals
\(1:3:5:...:(2n-1)\)
Velocity after successive equal time intervals
\(1:2:3:...:n\)
Time to reach successive equally spaced points
\(\sqrt1:\sqrt2:\sqrt3:...:\sqrt n\)
Time to cover successive equal distances
\((\sqrt1-\sqrt0):(\sqrt2-\sqrt1):(\sqrt3-\sqrt2):...:(\sqrt n-\sqrt{n-1})\)
▢ Motion Under Gravity:
❖ Free Fall from Height H:
◉ Conditions:
  • •
    \(u=0\)
  • •
    \(a=g\)
  • •
    \(s=H\)

Table 1: Freely Falling Body

Quantity
Formula
Time to reach ground
\(t=\sqrt{\frac{2H}{g}}\)
Velocity at height \(h\) above ground
\(v_1=\sqrt{2g(H-h)}\)
Striking velocity on ground
\(v=gt=\sqrt{2gH}\)
Average velocity for entire motion
\(\bar v=\frac{gt}{2}=\sqrt{\frac{gH}{2}}\)
Distance covered in \(n^{th}\) second
\(s_{nth}=\frac{g}{2}(2n-1)\)
◉ Distance Ratios:
  • •
    Distance covered in 1, 2, 3 seconds → \(1:4:9:...:n^2\)
  • •
    Distance covered in 1st, 2nd, 3rd seconds → \(1:3:5:...:(2n-1)\)
❖ Vertical Upward Projection:
◉ Conditions:
  • •
    At maximum height: \(v=0\)
  • •
    \(a=-g\)
  • •
    \(s=H\)

Table 1: Upward Projection Formulae

Quantity
Formula
Maximum height
\(H=\frac{u^2}{2g}\)
Time to reach maximum height
\(t=\frac{u}{g}=\sqrt{\frac{2H}{g}}\)
Total time of flight
\(T=2t=\frac{2u}{g}=\sqrt{\frac{8H}{g}}\)
Velocity at height \(h\)
\(v_1=\sqrt{2g(H-h)}=u\sqrt{1-\frac{h}{H}}\)
Average speed for complete upward-downward trip
\(\bar v=\frac{u}{2}=\sqrt{\frac{gH}{2}}\)
Average velocity for complete trip
0
Distance covered in last second of upward motion
\(h_n=u-\frac{g}{2}(2n-1)=\frac{g}{2}\)
◉ Point Passed Twice:

Table 1: If body passes height h at times t₁ and t₂

Quantity
Formula
Total time of flight
\(T=t_1+t_2\)
Time to maximum height
\(t=\frac{t_1+t_2}{2}\)
Maximum height
\(H=\frac{g(t_1+t_2)^2}{8}\)
Initial velocity
\(u=\frac{g(t_1+t_2)}{2}\)
Height of that point
\(h=\frac{g}{2}t_1t_2\)
❖ Smooth Inclined Plane:
◉ Condition: Body released from height \(h\) along smooth inclined plane of inclination \(\theta\)

Table 1: Inclined Plane Formulae

Quantity
Formula
Velocity at bottom
\(v=\sqrt{2gh}=\sqrt{2gl\sin\theta}\)
Acceleration down plane
\(a=g\sin\theta\)
Time to slide down
\(t=\sqrt{\frac{2l}{g\sin\theta}}=\sqrt{\frac{2h}{g}}\csc\theta\)
Same height, different inclinations
\(t\propto \csc\theta\)
Equal length, different inclinations
\(t\propto \sqrt{\csc\theta}\)
◉ Ratios:
  • •
    Same height → \(t_1:t_2:t_3=\csc\theta_1:\csc\theta_2:\csc\theta_3\)
  • •
    Equal length → \(t_1:t_2:t_3=\sqrt{\csc\theta_1}:\sqrt{\csc\theta_2}:\sqrt{\csc\theta_3}\)
▢ Accelerates then Retards:
❖ Condition: Particle accelerates from rest with acceleration \(\alpha\) for time \(t_1\), distance \(x_1\), then retards to rest with retardation \(\beta\) for time \(t_2\), distance \(x_2\)

Table 1: Acceleration-Retardation Formulae

Quantity
Formula
Ratio
\(\frac{\alpha}{\beta}=\frac{t_2}{t_1}=\frac{x_2}{x_1}\)
Net acceleration
\(a=\frac{\alpha\beta}{\alpha+\beta}\)
Total time
\(t=t_1+t_2=\sqrt{\frac{2s}{a}}=\sqrt{\frac{2(x_1+x_2)(\alpha+\beta)}{\alpha\beta}}\)
Maximum velocity
\(v_{max}=at=\frac{\alpha\beta}{\alpha+\beta}(t_1+t_2)\)
Total distance
\(s=x_1+x_2=\frac{1}{2}at^2=\frac{1}{2}\frac{\alpha\beta}{\alpha+\beta}(t_1+t_2)^2\)
▢ Relative Velocity:
❖ Definition: Velocity of A with respect to B = velocity with which A appears to move when B is brought to rest
❖ Formula: \(\vec v_{AB}=\vec v_A-\vec v_B\)
❖ Crossing Formula: \(T=\frac{Sum\ of\ lengths}{Relative\ velocity}\)
❖ Train Problems:

Table 1: Crossing Time

Case
Formula
Train length \(l_1\) crossing bridge length \(l_2\)
\(T=\frac{l_1+l_2}{v}\)
Two trains moving opposite directions
\(T=\frac{l_1+l_2}{v_1+v_2}\)
Two trains moving same direction
\(T=\frac{l_1+l_2}{v_1-v_2}\)
❖ River Crossing:
  • •
    Least time
  • •
    Least distance
▢ Read and Digest:

Table 1: Special Formulae

Case
Formula / Result
A person throws \(n\) balls per second; second ball when first is at highest point
Height of each ball = \(\frac{g}{2n^2}\)
Two ends of accelerating train pass point with velocities \(u\) and \(v\)
Velocity of middle point = \(\sqrt{\frac{u^2+v^2}{2}}\)
Escalator: moving time \(t_1\), standing time \(t_2\)
Walking time = \(\frac{t_1t_2}{t_1+t_2}\)
Falling body stopped after \(t_1\), then released and reaches ground after \(t_2\)
\(t^2=t_1^2+t_2^2\)
Thrown upward from height \(h\) reaches ground in \(t_1\); thrown downward reaches in \(t_2\); released reaches in \(t\)
\(t=\sqrt{t_1t_2}\)
Body starts from rest with uniform acceleration
\(\frac{Distance\ in\ n^{th}\ second}{Distance\ in\ n\ seconds}=\frac{2}{n}-\frac{1}{n^2}\)
Train at speed \(v\) sights another train ahead moving same direction with speed \(v'\), separation \(x\)
Minimum retardation formula incomplete in given note
▢ High-Yield Recall:

Table 1: Motion in Straight Line One-Liners

Fact
Answer
Straight-line motion
Rectilinear motion
Distance
Scalar path length
Displacement
Vector shortest distance with direction
Distance-displacement relation
\(Distance \geq |Displacement|\)
Speed
Rate of change of distance
Velocity
Rate of change of displacement
Acceleration
Rate of change of velocity
Average speed
\(\frac{Total\ distance}{Total\ time}\)
Average velocity
\(\frac{Total\ displacement}{Total\ time}\)
Instantaneous speed
\(\frac{dx}{dt}\)
Instantaneous velocity
\(\frac{d\vec s}{dt}\)
Instantaneous acceleration
\(\frac{d\vec v}{dt}\)
Uniform motion
\(s=ut\)
First equation
\(v=u+at\)
Second equation
\(s=ut+\frac{1}{2}at^2\)
Third equation
\(v^2=u^2+2as\)
Nth second distance
\(s_{nth}=u+\frac{a}{2}(2n-1)\)
Successive distances from rest
\(1:3:5:...\)
Distances up to successive seconds from rest
\(1:4:9:...\)
Free fall time from height H
\(\sqrt{\frac{2H}{g}}\)
Impact velocity in free fall
\(\sqrt{2gH}\)
Maximum height upward
\(\frac{u^2}{2g}\)
Time to maximum height
\(\frac{u}{g}\)
Total time of flight upward-return
\(\frac{2u}{g}\)
Average velocity for complete vertical up-down motion
0
Acceleration on smooth inclined plane
\(g\sin\theta\)
Velocity at bottom of smooth inclined plane
\(\sqrt{2gh}\)
Same-height inclined plane time
\(t\propto \csc\theta\)
Equal-length inclined plane time
\(t\propto \sqrt{\csc\theta}\)
Relative velocity
\(\vec v_{AB}=\vec v_A-\vec v_B\)
Opposite trains crossing
\(T=\frac{l_1+l_2}{v_1+v_2}\)
Same-direction trains crossing
\(T=\frac{l_1+l_2}{v_1-v_2}\)
Equal displacement average velocity
Harmonic mean
Equal time average velocity
Arithmetic mean
Q1.
If a lift of mass 1000 kg moves upward with acceleration of 1 m/s then tension is:
📅BP 2013
Q2.
A boy started his journey from home to school which 16 km far at uniform speed 2.5 Km/hr and while returning, he returned with 4km/hr. What is his average speed?
📅BP 2012
Q3.
Which is not graph of uniform motion:
📅BP 2012
Q4.
A person on a moving train throws upwards a coin, and if it falls behind him, then train is
📅BP 2012
Q5.
What is the total tension acting in figure?
📅BP 2012
Q6.
A boat was crossing the river with velocity 40 m/s and river flowing with velocity 30 m/s. Then resultant velocity was:
📅BP 2012
Q7.
If a lift of mass 500 Kg moves upward with acceleration 2 m/s then the tension is:
📅BP 2012
Q8.
A body moves along with constant acceleration. Then its graphical representation will be:
📅BP 2011
Q9.
A vehicle climbs a hill at speed of 40 km/hr and returns to same place at speed 60 km/hr. What is the average speed for whole journey?
Q10.
A man intends to cross a river on a boat with velocity 4 m/s. If resultant velocity of boat is 5 m/s. Then velocity of river is:
📅BP 2010
Q11.
Which of the following speed time graph is not possible?
📅BP 2009
Q12.
The slope of a velocity- time graph gives
📅MOE 2014
Q13.
Two bodies, one held I'm above the other directly, are released simultaneously and fall freely under gravity. After 3 second their relative separation will be
📅MOE 2013
Q14.
Time taken by a train of length 150 m and traveling with a uniform velocity of 6 km/hr to cross completely a bridge of length 1.5 km will be:
📅MOE 2013•MOE 2012
Q15.
A body is thrown vertically upward and attains a velocity 15 m/s at half the maximum height. The maximum height upto the body can reach will be:
📅MOE 2012•MOE 2011
Q16.
A body A is moving in north with 3 km/s and B with 4 km/s east. What is the relative velocity of a body A with respect to B.
📅MOE 2011
Q17.
A body moves 30m due north, 20m due east and 30sqrt(2) due south west. The total displacement covered by body from its initial position is:
📅I.E 2011
Q18.
Two bodies of mass '2 m' and 'm' are released from height '2H' and 'H' respectively. The ratio of time taken by\nthem to reach the ground is:
📅I.E 2011
Q19.
Two ships A and B are 4 km apart. A due west of B. If A moves with uniform velocity of 6 km/hr due south, calculate the magnitude of the velocity of A relative to B.
📅I.E 2013
Q20.
A body of mass 200 gm is thrown upwards with initial velocity of 30 m/s. What is total energy of body at height of 20 m from ground?
📅IOM 2014
Q21.
A body travels with velocity 30 m/s for 1st half of time and with velocity 40 m/s for 2nd half of time then what would be average velocity.
📅IOM 2013
Q22.
22. A body cover 1/3 rd distance with V1, velocity next 2/3 rd distance with V2 velocity the average velocity.
📅IOM 2012
Q23.
A person weighting 80 kg is standing on lift moves upward with a uniform acceleration of 4.9 m/s^2 then apparent wt. of the person is:
📅KU 2013•2012
Q24.
Two stones A and B are thrown from the top of a tower. The stone A is thrown vertically upward while the stone B is thrown vertically downward with the same speed. Which one of the following statements is true?
📅KU 2012
Q25.
25. A meter rod pivoted at its one end is rotated through 120degree. Then displacement of its free end will be.
📅IOM
Q26.
A person turns left or right by 90 after travelling each 20m in straight line. What is his maximum displacement after three successive turns?
Q27.
A person travels 3km towards north then 2km towards east and finally 2 sqrt(2) south-west. What is his displacement?
📅BPKIHS
Q28.
A flying kite travels 24m east then 8m south and finally 6m upward. What is its displacement from initial position?
Q29.
A racing car moving along circular track of radius R at constant speed v has described angle \\theta about centre of the track n certain time. What is the average velocity for the interval of time?
Q30.
A car travelling along circular track at constant speed 20m/s has completed half revolution on the track. Its average velocity will be
📅IOM/MOE/KU
Q31.
The length of a second hand in a watch is 1cm. The change in velocity in 15sec is
Q32.
If the displacement of a body is proportional to square of time. Then body has
📅IOM/I.E
Q33.
The displacement of a particle moving in a straight line at any instant time t is given as x = t^2 + 20 (in metre). What is its average velocity for first four seconds?
Q34.
In the above question, what is its velocity at 4 second?
Q35.
The acceleration of a particle at any instant of time 't' which starts from origin at initial velocity 2m/s is a = 2t (in m/s^2). What is its velocity in 5 seconds?
📅I.E
Q36.
A train of 150 meter length is going towards north direction at a speed of 1 m/sec. A parrot flies at the speed of 5m/sec towards south direction parallel to the railway track. The time taken by the parrot to cross the train is
Q37.
Two boys start running towards each other from two points, they are 120m apart. One runs with a speed of 5m/s and other with a speed of 7m/s. When and where do they meet each other from 1st point?
Q38.
A train of length 200m travelling at 30m/sec overtakes another train of length 300m travelling at 20m/sec. The time taken by first train to pass the second is
Q39.
An insect crawls a distance of 4m along north in 10seconds and then a distance of 3m along east in 5 seconds. The average velocity of the insect is:
Q40.
A vehicle moving along a straight road covers half distance of its journey a 40km/hr and next half distance at 60km/hr in same direction. The average velocity for entire journey is
📅IOM/MOE/KU/BPKIHS
Q41.
A vehicle moving along a straight road travels for half time at 40 km/hr and then travels for next half time at 60 km/hr. The average velocity for entire journey is
📅IOM/MOE/I.E/KU/BPKIHS
Q42.
A body moving in a straight line travels 2m/s for first half distance and second half distance is covered in two equal time intervals at 4m/s and 2m/s. What is its average velocity for entire journey?
Q43.
A body moving in a straight line travels 2m/s for first half time and for second half time it covers equal distance at velocities 4m/s and 2m/s. What is its average velocity for entire journey?
Q44.
A person travels certain distance x due east at constant velocity v, and then he travels equal distance x due north at constant velocity v2. What is his average velocity for entire journey?
📅IOM/MOE
Q45.
A person travels for certain time t due east at constant velocity v, and then he travels for equal time t due north at constant velocity v2. What is his average velocity for entire journey?
📅IOM
Q46.
The displacement of a particle is given by x = 2 -5t + 6t^2 where x is in meters and t in seconds. The initial velocity of the particle
Q47.
If x denotes displacement in time t, and x = a cost, the acceleration is
Q48.
A car travelling due east at 20m/s turns towards north without changing speed in 10sec. The average acceleration of the car for its turn is
Q49.
In the above question if the car makes 'U' turn then average acceleration of the car will be
Q50.
A car travelling due north at 30km/hr turns west and travels at the same speed, the change in velocity of car is [MOE 2066]
Q51.
A body starts from rest and moves at constant acceleration a in a straight line for time t1, covering a distance x1, and then it retards at rest at constant deceleration b for time t2 covering a distance X2. Then average velocity will be
Q52.
A stone is dropped from the top of a tower. If it reaches the earth in 6 seconds, the height of the tower is nearly.
📅BPKIHS
Q53.
A car accelerates from rest at constant rate for the first 10seonds and covers a distance x. It covers a distance y in the next 10 seconds at the same acceleration. Which of the velocity is true?
📅BPKIHS
Q54.
A car accelerates at a constant rate a1 for time t1 and then retards at the constant\nrate a2 for time t2 and comes to rest t1/t2 =
Q55.
55. A person is throwing balls into the air one after the other. He throws the second ball when first ball is at the highest point. If he is throwing two balls every second, how high do they rise?
Q56.
A ball is dropped from the top of a tower 100m high. Simultaneously, another ball is thrown upwards with a speed of 50m/s. After what time do they cross each other?
Q57.
The engine of a motorcycle can produce a maximum acceleration 5m/s. Its brakes can produce a maximum retardation 10 m/s^2. What is the minimum time in which it can cover a distance of 1.5 km?
Q58.
Two balls A and B are simultaneously projected from the top of a building at 10m/s upwards and 20m/s downwards respectively. Find out the separation between them 3sec after projection.
Q59.
59.A stone is dropped from a certain height which can reach the ground is 5 second. It is stopped after three second of its fall and then is again released. The total time taken by the stone to reach the ground will be
Q60.
A balloon is going upwards with velocity 12m/s. It releases a packet when it is a height of 65m from ground. How much time will the packet take to reach the ground (g = 10m/s^2)?
Q61.
A car moving with a speed of 40km/hr can be stopped by applying brakes after at least 2m. If the same car is moving with speed of 80 km/hr, the minimum stopping distance is
Q62.
A ball is dropped from the top of a very high tower. Distance covered by it in last second of its motion equal to the distance covered by in first 3secs of its motion. Find the time of fall
Q63.
A ball thrown vertically upward covers equal distances in its fourth and fifth second. Then initial velocity of projection will be
Q64.
A ball is projected vertically upwards from the ground. It is found at the same elevation at t = 3s and t = 7s after projection. Find the projection speed.
Q65.
A stone is dropped from the top of a tower. If it covers 24.5m in the last second of its motion, the height of the tower is
Q66.
A body is projected vertically upward from point A, the top of a tower. It reaches the ground in t1 secs. If it is projected vertically downwards from A with the same velocity, it reaches the ground in t2 secs. If it falls freely from A, it would reach the ground in
Q67.
A body is released from top of a smooth inclined plane having inclination 30degree and takes 3secs to reach the bottom. If the angle of inclination is doubled keeping the height same, what will be the time taken for the same process?
Q68.
A body sliding on a smooth inclined plane requires 4 seconds to reach the bottom, starting from rest at the top. How much time does it take to cover one-fourth distance starting from rest at the top? [KU]
Q69.
A ball is dropped from the top of a building and its time of fall is 't'. In the last 1/4^th time of its fall, it travels 1.4 metres. Find out the height of the building
Q70.
A ball is projected vertically upwards from ground and its time of rise is 't'. In first t/5 time, it covers a distance of 2.7m. Find the height
Q71.
A body is thrown upwards with velocity 100m/s and it travels 5m in the last second of its upward journey. If the same body is thrown upwards with velocity 200m/s, what distance will it travel in the last second of upward journey?
Q72.
A body falls freely from rest and has velocity v after it falls through a height h. The distance it has to fall down further for its velocity to become double is
Q73.
A ball dropped downwards. After 1 second another ball is dropped downwards from the same point. What is the distance between them 3seconds after the first ball was dropped?
Q74.
Two bodies are thrown vertically upward with their initial velocities in ratio 2: 3. Then the ratio of maximum heights attained by them is
Q75.
A lion chases a deer 30m ahead of it and gains 3m in as alter the chase started. After 10s, the distance between them is
Q76.
A ball A is thrown vertically upward at initial speed u while another B is dropped from a height at the same instant. After time t, their relative velocity w.r.t one another will be
Q77.
A stone dropped from a height covers 5/9 part of total distance in last second. Then initial height will be
Q78.
Water drops are falling at regular intervals of time from a roof 5m high. When first drop strikes the ground, third drop just leaves the roof then height of the second drop from the ground at this\ninstant is
Q79.
A body thrown vertically upwards attains a maximum height H. While moving upwards if it covers first (3H/4) distance from the ground in time T, then time taken to cover remaining distance H/4 will be
📅IOM/MOE/KU/BPKIHS
Q80.
When a ball is thrown upwards with air resistance not neglected, it takes 10seconds to reach a height. It then returns to ground in time. [MOE]
Q81.
A bullet loses 1/20 of its velocity after penetrating a plank. How may planks are required to stop the bullet?
Q82.
Three particles A, B and C are situated at the vertices of an equilateral triangle ABC of side l at t = 0. Each of the particle moves with constant speed v. A always has its velocity along AB, B along BC and C along CA. At what time will these particles meet each other?
Q83.
A vehicle moving at constant acceleration along a straight road has velocities u and v at two point A and B on the road. Then it velocity at midway between A and B will be
Q84.
A person who can swim at 5km/hr in still water, crosses a river 1 km wide flowing at 3km/hr along shortest route. Then time taken to cross the river is
Q85.
A person who can swim at 12km/hr in still water wants to cross a river flowing at 6km/hr along shortest route. Then he has to start swimming at
Q86.
A person who can swim at 5km/hr in still water cross a river 1km wide flowing at 3km/hr in shortest time. How far he will reach at another bank?
Q87.
To a person running due east at 8km/hr raindrops appear to fall vertically downward at 6km/hr. Then actual velocity of raindrops is
Q88.
A boat takes 2 hours to travel 8km and back in still water lake. If the velocity of water is 4km/hr, the time taken for going upstream of 8km and coming back is
Q89.
A stone is dropped from the top of a tower of height 'h'. It reaches the ground in 't' secs. The position of the stone after t/3 secs. will be ... from the ground [IOM 063]
Q90.
A stone is dropped from the top of tower of height h. After 1 second another stone is dropped from balcony 20 m below the top. Both reach the bottom simultaneously. What is the value of h?\n[IOM 05]
Q91.
A body of mass 'm' is released from height 'h' in time 't'. Then, acceleration is determined by:\n[IOM 2015)
Q92.
When an aeroplane is moving with velocity 600km/h due east & return with 400km/hr,\nthen what is average speed if they travel same distance? [KU 2016)
Q93.
A person is traveling at 4 m/s towards east. The rain is apparently falling vertically downwards with 3 m/s, then the actual velocity of rain is, [IOM 2016]
Q94.
A train travels for 40 km with velocity of 80 km/hr and again it travels next 40 km with velocity of 40 km/hr. Then average speed of the train is [IOM 2016]