A body is travelling with uniform acceleration and travels 84 m in first 6 seconds and 180 m in the next 5 seconds. Find the initial velocity and acceleration of the body.

Let initial velocity u and acceleration is a.

For the first part of motion traveled 84 m in 6 seconds. By equation,

s = ut +i/2at∧2

The above kinetic equation gives the following equation

6u + 18a = 84 …..(1)

The final velocity at the end of 6 seconds is

u6 = u+6a, where u6 is velocity after 6 seconds

After using velocity relation after 6 seconds in the second part of the motion we get the following equation

(u+6a)5 + ½× a× 25 = 180

By simplification we will get :- 5u + (85/2)a = 180……..(2)

By solving equations (1) and (2) we get

a = 2 m/s2 , u = 4 m/s

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