A body starts with an initial velocity of 10 m s and acceleration 5 m s 2 . Find the distance covered by it in 5 s .

Given: u = 10 m s ; a = 5 m s 2 ; t = 5 s ; s = ? Distance travelled, s = u t + 1 2 a t 2 = 10 × 5 + 1 2 ( 5 ) ( 5 ) 2 = 50 + 62 . 5 = 112 . 5 m

A vehicle is accelerating on a straight road. Its velocity at any instant is 30 k m h , after 2 s , it is 33 . 6 k m h and after further 2 s , it is 37 . 2 k m h . Find the acceleration of vehicle in m s 2 . Is the acceleration uniform?

We know that acceleration = Rate of change of velocity Velocity in the first 2 s is 33 . 6 k m h &there4; Acceleration 33 . 6 - 30 2 = 3 . 6 2 = 1 . 8 k m h 2 Converting k m h 2 to m s 2 1 . 8 × 1000 60 × 60 = 0 . 5 m s 2 Further velocity after 2 s is 37 . 2 k m h &there4; Acceleration = 37 . 2 - 33 . 6 2 = 3 . 6 2 = 1 . 8 k m h 2 Converting k m h 2 to m s 2 1 . 8 × 1000 60 × 60 = 0 . 5 m s 2 Comparing acceleration from both instances it can be said that the acceleration is uniform.

A body initially at rest, starts moving with a constant acceleration 2 m s 2 . Calculate the velocity acquired in 5 s .

Given: a = 2 m s 2 , u = 0 m s ; t = 5 s ; v = ? v = u + a t = 0 + 2 × 5 v = 10 m s

A body initially at rest, starts moving with a constant acceleration 2 m s 2 . Calculate the distance travelled in 5 s .

Given: a = 2 m s 2 , u = 0 m s , t = 5 s s = u t + 1 2 a t 2 = 0 ( 5 ) + 1 2 ( 2 ) ( 5 ) 2 = 0 + 25 = 25 Distance travelled = 25 m

A train moving with a velocity of 20 m s is brought to rest by applying brakes in 5 s . Calculate the retardation.

Given: u = 20 m s ; v = 0 ; t = 5 s ; a = ? We know that acceleration = v - u t = ( 0 - 20 ) 5 = - 4 m s 2 ∴ Retardation is 4 m s 2

A train travels with a speed of 60 k m h from station A to station B and then comes back with a speed 80 k m h from station B to station A . Find the average speed.

Assume d be the distance between station A and station B . Average speed = t o t a l d i s t a c n e t r a v e l l e d t o t a l t i m e t a k e n Total distance travelled = d + d = 2 d Total time taken = travel time from station A to B + travel time from station B to A = d 60 + d 80 = 140 d 4800 V a v = t o t a l d i s t a c n e t r a v e l l e d t o t a l t i m e t a k e n = 2 d 140 d 4800 = 2 × 4800 140 = 68 . 57 k m h

A train travels with a speed of 60 k m h from station A to station B and then comes back with a speed 80 k m h from station B to station A . Find the average velocity of train.

To find the average velocity, displacement should be known; As we know, A v e r a g e v e l o c i t y = t o t a l d i s p l a c e m e n t t o t a l t i m e t a k e n Since the train starts the journey and end the journey at the same station, the displacement is zero, the average velocity is also zero.