# How to Find Velocity With Non-Constant Acceleration

1. Sep 24, 2012

### Ellipses

Hi everyone. I don't want someone to do the question so I won't include my actual homework question, but I would really appreciate if someone would tell me how to find velocity after a time t if your acceleration is non-constant and time dependent.

For example, if your acceleration was a = 4.0t and you want to find velocity after 3.0 seconds, how would you do that? Thank you!

2. Sep 24, 2012

### Curious3141

Have you learnt calculus yet? You need to integrate the acceleration with respect to time, while setting the lower bound to 0 (seconds) and the upper bound to 3 (seconds), i.e.

$$v(3) = \int_0^3 a(t) dt = \int_0^3 4t dt$$

Here, v(t) refers to velocity as a function of time, so v(3) is velocity at time 3 seconds. a(t) is acceleration as a function of time.

3. Sep 24, 2012

### Ellipses

Thanks for the answer! I know indefinite integrals but not definite so could you please explain how you solve your example? (: