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_O.The distance traveled by the particle in time t will be?

Answer 1

`d(t) = 1/6bt^3+V_0t`

Explanation:

Given the acceleration as a function of time:

`a(t) = bt`

Integrate to obtain the velocity as a function of time.

`v(t) = 1/2bt^2+C`

We are told that the constant of integration is `V_0`

`v(t) = 1/2bt^2+V_0`

Integrate, again, to obtain the displacement as a function of time.

`d(t) = 1/6bt^3+V_0t+C`

The phrase "starts from the origin" tells us that the integration constant is 0:

`d(t) = 1/6bt^3+V_0t`