# How do you find the distance travelled from t=0 to t=1 by a particle whose motion is given by #x=4(1-t)^(3/2), y=2t^(3/2)#?

##### 1 Answer

You can integrate the speed of travel to get a distance of

#### Explanation:

The speed is the length of the velocity vector. It is equal to

We differentiate to get

Therefore,

The distance traveled is therefore

This integral can be done by the substitution

Now use the Fundamental Theorem of Calculus to get