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?

1 Answer
Feb 23, 2018

#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#