# Integral for velocity

1. Oct 26, 2015

### 24forChromium

1. The problem statement, all variables and given/known data
An object is initially at rest, then, it receives a various acceleration a.
The acceleration is a function of its displacement d, given by the function a = cos (d/5 metre)
What is the object's velocity after moving 3 metres?

2. Relevant equations
d = 0.5*a^2
a = cos(d/5m) (question specific)

3. The attempt at a solution
This probably requires integration, of which I have basic understandings.

(Oh by the way, this is originally a problem dealing with a catapult, where the catapult's shaft is receiving a torque that varies with time (gravity's direction is unchanged but the tangent's direction does change) and I needed to calculate the final angular velocity after the shaft rotates a certain amount of angles. I thought the principle applies to linear motion too.)

Last edited: Oct 26, 2015
2. Oct 26, 2015

### BvU

Your relevant equation (single) is valid for constant acceleration, so it does not apply here. You will have to revert to the definition of acceleration and (as you already suspected) have to do an integration. Make a first step: what has to be integrated ?

 Oops , as Andrew hints, your equation isn't even complete !

Last edited: Oct 26, 2015
3. Oct 26, 2015

### andrewkirk

Where did you get that equation? Check the source.