# When we integrate function of acceleration, what do we get?

1. Nov 4, 2013

### AakashPandita

Do we get function for velocity or do we get the function for the total change in velocity?

2. Nov 4, 2013

### HallsofIvy

What kind of integral do you mean? The "indefinite integral" is a function, the "definite integral" is a number. The "indefinite integral" of the acceleration function, $\int a(t)dt$ is the velocity function, v(t), plus a "constant of integration". The definite integral, $\int_{t_0}^{t_1} a(t)dt= v(t_1)- v(t_0)$, change in speed between times $t_0$ and $t_1$.

We can combine the two: writing $\int_{t_0}^T a(t)dt$ where $t_0$ is a fixed time and T is a variable. It gives, for any T, the change in velocity since time $t_0$.

Last edited by a moderator: Nov 4, 2013
3. Nov 4, 2013

### AakashPandita

okay. thanks again!

4. Nov 4, 2013

### AakashPandita

you said it tells us the change in speed.
that means we do not get direction of change?

5. Nov 4, 2013

### vanhees71

Warning: All you wrote is correct for the vector quantities $\vec{v}$ and $\vec{a}$ but in general not for the magnitudes!

6. Nov 4, 2013

### AakashPandita

?i don't understand.