# Motions Question (1 Viewer)

#### kevda1st

##### Member
These are problems from the flitzpatrick book

1. A body falls from rest in a medium and its velocity v at any time t is given by
v=49(1-e^-0.5t)
find the distance fallen in the first 5 seconds

#### jet

##### Banned
$\bg_white \text{Since velocity is the derivative of distance, we can integrate over the velocity function to find distance travelled: } \\ d = 49\int^5_0 1 - e^{-0.5t} \, dt \\ = 49 \left [t + 2e^{-0.5t} \right ]^5_0 \\ = 49[5 + 2e^{-2.5} - 0 - 2] \\ = 49[3 + \frac{2}{e^{2.5}}] = 155m$

I'm quite sure that's right. Tell me if it isnt.

#### ghostman_on_3rd

##### Member
ye i got i got 155units also