# How to Find Velocity With Non-Constant Acceleration

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!

## Answers and Replies

Homework Helper
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!

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.

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