A staircase contains three steps each 10cm high and 20cm wide (figure). What should be the minimum horizontal velocity of a ball rolling off the uppermost plane so as to hit directly the lowest plane?
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Rest and Motion: Kinematics question types
94 questions across 6 question groups — pick any mix to generate a Physics paper with step-by-step answer keys.
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10 Q→Sample Questions
Rest and Motion: Kinematics questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
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The speed of a car as a function of time is shown in figure. Find the distance travelled by the car in 8 seconds and its acceleration.
Figure shows x-t graph of a particle. Find the time t such that the average velocity of the particle during the period 0 to t is zero.
A particle starting from rest moves with constant acceleration. If it takes 5.0s to reach the speed 18.0km/h find:
- The average velocity during this period.
- The distance travelled by the particle during this period.
A driver takes 0.20s to apply the brakes after he sees a need for it. This is called the reaction time of the driver. If he is driving a car at a speed of 54km/h and the brakes cause a deceleration of 6.0m/s2, find the distance travelled by the car after he sees the need to put the brakes on.
The acceleration of a cart started at t = 0, varies with time as shown in figure. Find the distance travelled in 30 seconds and draw the position-time graph.
Suppose A and B in the previous problem change their positions in such a way that the line joining them becomes perpendicular to the direction of wind while maintaining the separation x. What will be the time lag B finds between seeing and hearing the drum beating by A?
A ball is dropped from a height. If it takes 0.200s to cross the last 6.00m before hitting the ground, find the height from which it was dropped. Take g = 10m/s2.
A ball is dropped from a balloon going up at a speed of 7m/s. If the balloon was at a height 60m at the time of dropping the ball, how long will the ball take in reaching the ground?
Find the average velocity of a projectile between the instants it crosses half the maximum height. It is projected with a speed u at an angle $\theta$ with the horizontal.
View full solution →An object having a velocity 4.0m/s is accelerated at the rate of 1.2m/s2 for 5.0s. Find the distance travelled during the period of acceleration.
A person travelling at 43.2km/h applies the brake giving a deceleration of 6.0m/s2 to his scooter. How far will it travel before stopping?
A particle starts from a point A and travels along the solid curve shown in figure. Find approximately the position B of the particle such that the average velocity between the positions A and B has the same direction as the instantaneous velocity at B.
An NCC parade is going at a uniform speed of 6km/h through a place under a berry tree on which a bird is sitting at a height of 12.1m. At a particular instant the bird drops a berry. Which cadet (give the distance from the tree at the instant) will receive the berry on his uniform?
Figure shows the graph of the x-coordinate of a particle going along the X-axis as a function of time. Find:
- The average velocity during 0 to 10s.
- Instantaneous velocity at 2, 5, 8 and 12s.
Two friends A and B are standing a distance x apart in an open field and wind is blowing from A to B. A beats a drum and B hears the sound t1 time after he sees the event. A and B interchange their positions and the experiment is repeated. This time B hears the drum t2 time after he sees the event. Calculate the velocity of sound in still air v and the velocity of wind u. Neglect the time light takes in travelling between the friends.
An elevator is descending with uniform acceleration. To measure the acceleration, a person in the elevator drops a coin at the moment the elevator starts. The coin is 6ft above the floor of the elevator at the time it is dropped. The person observes that the coin strikes the floor in 1 second. Calculate from these data the acceleration of the elevator.
A police jeep is chasing a culprit going on a motorbike. The motorbike crosses a turning at a speed of 72km/h. The jeep follows it at a speed of 90km/h, crossing the turning ten seconds later than the bike. Assuming that they travel at constant speeds, how far from the turning will the jeep catch up with the bike?
Two friends A and B are standing a distance x apart in an open field and wind is blowing from A to B. A beats a drum and B hears the sound t1 time after he sees the event. A and B interchange their positions and the experiment is repeated. This time B hears the drum t2 time after he sees the event. Calculate the velocity of sound in still air v and the velocity of wind u. Neglect the time light takes in travelling between the friends.
A player hits a baseball at some angle. The ball goes high up in space. The player runs and catches the ball before it hits the ground. Which of the two (the player or the ball) has greater displacement?
In the arrangement shown in figure, the ends P and Q of an inextensible string move downwards with uniform speed u. Pulleys A and B are fixed. The mass M moves upwards with a speed: 
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$2\text{u}\cos\theta$
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$\frac{\text{u}}{\cos\theta}$
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$\frac{\text{2u}}{\cos\theta}$
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$\text{u}\cos\theta$
A person travelling on a straight line moves with a uniform velocity v1 for some time and with uniform velocity v2 for the next equal time. The average velocity is given by:
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$\text{v}=\frac{\text{v}_1+\text{v}_2}{2}$
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$\text{v}=\sqrt{\text{v}_1\text{v}_2}$
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$\frac{2}{\text{v}}=\frac{1}{\text{v}_1}+\frac{1}{\text{v}_2}$
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$\frac{1}{\text{v}}=\frac{1}{\text{v}_1}+\frac{1}{\text{v}_2}$
A person travelling on a straight line moves with a uniform velocity v1 for a distance x and with a uniform velocity v2 for the next equal distance. The average velocity v is given by:
View full solution →-
$\text{v}=\frac{\text{v}_1+\text{v}_2}{2}$
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$\text{v}=\sqrt{\text{v}_1\text{v}_2}$
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$\frac{2}{\text{v}}=\frac{1}{\text{v}_1}+\frac{1}{\text{v}_2}$
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$\frac{1}{\text{v}}=\frac{1}{\text{v}_1}+\frac{1}{\text{v}_2}$
The velocity-time plot for a particle moving on a straight line is shown in the figure:
- The particle has a constant acceleration.
- The particle has never turned around.
- The particle has zero displacement.
- The average speed in the interval 0 to 10s is the same as the average speed in the interval 10s to 20s.
Mark the correct statements for a particle going on a straight line:
- If the velocity and acceleration have opposite sign, the object is slowing down.
- If the position and velocity have opposite sign, the particle is moving towards the origin.
- If the velocity is zero at an instant, the acceleration should also be zero at that instant.
- If the velocity is zero for a time interval, the acceleration is zero at any instant within the time interval.
An aeroplane has to go from a point A to another point B, 500km away due 30° east of north. A wind is blowing due north at a speed of 20m/s. The air-speed of the
plane is 150m/s.
plane is 150m/s.
- Find the direction in which the pilot should head the plane to reach the point B.
- Find the time taken by the plane to go from A to B.
A car travelling at 60km/h overtakes another car travelling at 42km/h. Assuming each car to be 5.0m long, find the time taken during the overtake and the total road distance used for the overtake.
Consider the situation of the previous problem. The man has to reach the other shore at the point directly opposite to his starting point. If he reaches the other shore somewhere else, he has to walk down to this point. Find the minimum distance that he has to walk.
A ball is thrown horizontally from a point 100m above the ground with a speed of 20m/s. Find:
- The time it takes to reach the ground.
- The horizontal distance it travels before reaching the ground.
- The velocity (direction and magnitude) with which it strikes the ground.
A train starts from rest and moves with a constant acceleration of 2.0m/s2 for half a minute. The brakes are then applied and the train comes to rest in one minute. Find:
- The total distance moved by the train.
- The maximum speed attained by the train.
- The position(s) of the train at half the maximum speed.
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