Question

A particle starts with initial velocity 4m/s and moves with a = V ^1/2

Answer 1

The question is incomplete.

Still assuming if displacement is being asked.

The equation goes like displacement = u + a / 2 × ( 2 n - 1 ).

Putting down the values in the equation, the answer for the displacement will be 13. 5 m .

Although the question is not clear, this is my answer.

Answer 2

Answer:(i) v=9m/s

(ii) v=16m/s

Explanation: GIVEN:- u=4m/s and acceleration a given by a=√v

(i) => We know that, a=v.dv/dx. (x for displacement)

Therefore, v.dv/dx = v^½

v^½dv =dx

Integerating both sides, we get

(2v^3/2)/3 = x + c (where, c is constant)

At x=0. v=4m/s

Therefore, 2(4^3/2)/3 =0 + c

C= 16/3.

At x=38/3 , v=?

2(v^3/2)/3 = 38/3 +16/3

√v³ = 27 ==> v³=27²

Therefore, v = 9m/s

(ii) a=√v

dv/dt=v½==> dv/v½ = dt

Integrating both sides , we get

2v½ = t+ d (where d is constant)

At t=0 , v=4m/s

2*4½= d

d= 4.

At t=4 sec , v=?

2(v½) =4+4

√v = 4

Therefore, v= 16m/s