# The acceleration of a particle increasing linearly with time 𝑡 is 𝑏𝑡. The particle starts from the origin with an initial velocity 𝑣0. The distance travelled by the particle in time 𝑡 will be

Question : The acceleration of a particle increasing linearly with time 𝑡 is 𝑏𝑡. The particle starts from the origin with an initial velocity 𝑣0. The distance travelled by the particle in time 𝑡 will be

(A) $v_{0}t+\dfrac{1}{6}bt^{3}$

(B) $v_{0}t+\dfrac{1}{3}bt^{2}$

(C) $v_{0}t+\dfrac{1}{3}bt^{3}$

(D) $v_{0}t+\dfrac{1}{6}bt^{2}$