What is the equation for calculating displacement based on acceleration?

[24forChromium]

Homework Statement

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?

Homework Equations

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

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.)

 

[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 ?

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

 

[andrewkirk]

Homework Equations

d = 0.5*a^2

Where did you get that equation? Check the source.