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 ).

The names of 5 students from section A, 6 students from section B and 7 students from section C were selected. The age of all the 18 students was different. Again, one name was selected from them and it was found that it was of section B. What was the probability that it was the youngest student of the section B?

A bag contains 35 balls of three different colors viz. red, orange and pink. The ratio of red balls to orange balls is 3 : 2, respectively and probability of choosing a pink ball is 3/7. If two balls are picked from the bag, then what is the probability that one ball is orange and one ball is pink?

There are total 18 balls in a bag. Out of them 6 are red in colour, 4 are green in colour and 8 are blue in colour. If Vishal picks three balls randomly from the bag, then what will be the probability that all the three balls are not of the same colour?