Show that area under velocity - time graph is equal to displacement.

What is the significance of velocity - time graph?

Derive the equations of motion (i) \(v= v_0 + at\) and (ii) \(v^2 = v_0^2 +2ax\) from v - t graph.

Derive the equations of motion (i) \(v= v_0 + at\) and (ii) \(v^2 = v_0^2 +2ax\) from v - t graph.

A car moving along a straight highway with speed of 126 km h^-1 to brought to stop within a distance of 200 m. What is the retardation of the car and how long does it take for the car to stop?

A car starts from rest and accelerates uniformly at a rate of 2 ms^-1 for 20 second. It then maintains a constant velocity for 10 second. The brakes are then applied and the car is uniformly retarded and comes to rest in 5 second. Draw the velocity - time graph for the motion and find :

(i) the maximum velocity

(ii) the retardation in the last 5 second

(iii) total distance traveled and (iv) average velocity.

A stone is dropped from the top of a tower 400 m high and at the same time another stone is projected upward vertically from the ground with a velocity of 100 ms^-1 . Find where and when the two stones will meet.

Two trains are moving in opposite directions. Train A moves east with a speed of 10 ms^-1 and train B moves west with a speed of 20 ms^-1 . What is the

(i) relative velocity of B w.r.t A and

(ii) the relative velocity of ground w.r.t B.

(iii) A dog is running on the roof of train A against its motion with a velocity of 5 ms^-1 w.r.t train A. What is the velocity of the dog as observed by a man standing on the ground?

Two trains A and B of length 200 m each are moving on two parallel tracks with a uniform speed of 10 ms^-1 in the same direction, with the train A ahead of B. The driver of train B decides to overtake train A and accelerates by 1 ms^-2. If after 50 s, the guard of train B brushes past the driver of train A, what was the original distance between the two trains?

A body is thrown vertically up from the top of a building with a velocity of 10 ms^-1 . It reaches the ground in 5 s. Find the height of the building and the velocity with which the body reaches the ground. (g = 10 ms^-2 ).