How Do You Calculate Velocity Change with Time-Dependent Acceleration?

[Ginerva123]

Homework Statement

The acceleration of a bus is given by , a(t) = xa where x = 1.24 m/s3 is a constant. If the bus's velocity at time t1 = 1.15s is 4.94 m/s, what is its velocity at time t2 = 2.10s ?

Homework Equations

I know I have to integrate somehow, but the only equation I can think of to apply is
v(t) = v (initial) + integral of [a dt] with boundaries t and 0.

The Attempt at a Solution

I tried using the basic equations of motion, but they all assume that acceleration is constant... then I tried the above equation but I'm having trouble finding the intial velocity. Please help!

 

[rl.bhat]

The value of x = 1.24m/s^3 Therefore 'a' must be time t. Integrate the function wrt. time. Using t1 and the velocity find the constant of integration. Now put t2 = 2.1s and find the velocity.