Rest and Motion: Kinematics Physics - Rest and Motion: Kinematics

A river is flowing from west to east at a speed of 5 metres per minute. A man on the south bank of the river, capable of swimming at 10 metres per minute in still water, wants to swim across the river in the shortest time. He should swim in a direction:

1. Due north.
2. 30° east of north.
3. 30° north of west.
4. 60° east of north.

The velocity-time plot for a particle moving on a straight line is shown in the figure:

1. The particle has a constant acceleration.
2. The particle has never turned around.
3. The particle has zero displacement.
4. 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:

1. If the velocity and acceleration have opposite sign, the object is slowing down.
2. If the position and velocity have opposite sign, the particle is moving towards the origin.
3. If the velocity is zero at an instant, the acceleration should also be zero at that instant.
4. If the velocity is zero for a time interval, the acceleration is zero at any instant within the time interval.

The accelerations of a particle as seen from two frames S₁ and S₂ have equal magnitude 4m/s².

1. The frames must be at rest with respect to each other.
2. The frames may be moving with respect to each other but neither should be accelerated with respect to the other.
3. The acceleration of S₂ with respect to S₁ may either be zero or 8m/s².
4. The acceleration of S₂ with respect to S₁ may be anything between zero and 8m/s.

Figure shows the position of a particle moving on the X-axis as a function of time.

1. The particle has come to rest 6 times.
2. The maximum speed is at t = 6s.
3. The velocity remains positive for t = 0 to t = 6s.
4. The average velocity for the total period shown is negative.

Galileo was punished by the Church for teaching that the sun is stationary and the earth moves around it. His opponents held the view that the earth is stationary and the sun moves around it. If the absolute motion has no meaning, are the two, viewpoints not equally correct or equally wrong?

A car travels at a speed of 60km/hr due north and the other at a speed of 60km/hr due east. Are the velocities equal? If no, which one is greater? If you find any of the questions irrelevant, explain.

The increase in the speed of a car is proportional to the additional petrol put into the engine. Is it possible to accelerate a car without putting more petrol or less petrol into the engine?

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.

Figure shows the graph of the x-coordinate of a particle going along the X-axis as a function of time. Find:

1. The average velocity during 0 to 10s.
2. Instantaneous velocity at 2, 5, 8 and 12s.

If a particle is accelerating, it is either speeding up or speeding down. Do you agree with this statement?

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:

1. The average velocity during this period.
2. 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.

From the velocity-time plot shown in figure, find the distance travelled by the particle during the first 40 seconds. Also find the average velocity during this period.

popular game in Indian villages is goli which is played with small glass balls called golis. The goli of one player is situated at a distance of 2.0m from the goli of the second player. This second player has to project his goli by keeping the thumb of the left hand at the place of his goli, holding the goli between his two middle fingers and making the throw. If the projected goli hits the goli of the first player, the second player wins. If the height from which the goli is projected is 19.6cm from the ground and the goli is to be projected horizontally, with what speed should it be projected so that it directly hits the stationary goli without falling on the ground earlier?

A person sitting on the top of a tall building is dropping balls at regular intervals of one second. Find the positions of the 3^rd, 4^th and 5^th ball when the 6^th ball is being dropped.

A person standing on the top of a cliff 171ft high has to throw a packet to his friend standing on the ground 228ft horizontally away. If he throws the packet directly aiming at the friend with a speed of 15.0ft/s, how short will the packet fall?

A particle starts from the origin, goes along the X-axis to the point (20m, 0) and then returns along the same line to the point (-20m, 0). Find the distance and displacement of the particle during the trip.

A ball is projected vertically upward with a speed of 50m/s. Find:

1. The maximum height.
2. The time to reach the maximum height.
3. The speed at half the maximum height. Take g = 10m/s².

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.

Complete the following table:

Car Model	Driver X Reaction time 0.20s	Driver Y Reaction time 0.30s
A (deceleration on hard braking = 6.0m/s2)	Speed = 54km/h Braking distance a = ... Total stopping distance b = ...	Speed = 72km/h Braking distance c = ... Total stopping distance d = ...
B (deceleration on hard braking = 7.5m/s2)	Speed = 54km/h Breaking distance e = ... Total stopping distance f = ...	Speed 72km/h Braking distance g = ... Total stopping distance h = ...

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?

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.

It is 260km from Patna to Ranchi by air and 320km by road. An aeroplane takes 30 minutes to go from Patna to Ranchi whereas a delux bus takes 8 hours.

1. Find the average speed of the plane.
2. Find the average speed of the bus.
3. Find the average velocity of the plane.
4. Find the average velocity of the bus.

A ball is dropped from a height of 5m onto a sandy floor and penetrates the sand up to 10cm before coming to rest. Find the retardation of the ball in sand assuming it to be uniform.

The benches of a gallery in a cricket stadium are 1m wide and 1m high. A batsman strikes the ball at a level one metre above the ground and hits a mammoth sixer. The ball starts at 35m/s at an angle of 53° with the horizontal. The benches are perpendicular to the plane of motion and the first bench is 110m from the batsman. On which bench will the ball hit?

A person is standing on a truck moving with a constant velocity of 14.7m/s on a horizontal road. The man throws a ball in such a way that it returns to the truck after the truck has moved 58.8m. Find the speed and the angle of projection:

1. As seen from the truck.
2. As seen from the road.

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.