Question

The acceleration of a particle is increasing linearly with time t as bt .the particle starts from the origin with an initial velocity v*. The distance traveled by the particle in time t will be?

Answer 1

Answer:

The distance traveled by the particle in time t will be $bt^{3}/6$+v*t.

Explanation:

We know that a=bt.

Integrating it we get,

$\int\limits^0_ v{} \, dv=\int\limits^0_t {bt} \, dt$

v = $bt^{2}/2$+C

At t = 0, v= v*

So, c=v*.

v=$bt^{2}/2$+v*

Integrating again we get,

x=$bt^{3}/6$+v*t +C

at t=  0 , x= 0, So C=0

The answer is  x=$bt^{3}/6$+v*t