Mathematics

Problem

The acceleration of a particle is increasing linearly with time

t

bt

. The particle starts from the origin with an initial velocity

v_0

. The distance travelled by the particle in time

t

will be (A)

v_0t + \frac{1}{3}bt^2

(B)

v_0t + \frac{1}{3}bt^3

(C)

v_0t + \frac{1}{6}bt^3

(d)

v_0t + \frac{1}{2}bt^3