Calculating velocity and position with integrals

Asked Mar 11 '21 at 19:25

Active Mar 11 '21 at 19:36

Viewed 30 times

A ball is dropped from a height of 3000 feet. Its velocity after t seconds is $v(t)=-78t$.

a) How fast is the ball dropping after 5 seconds?

b) Determine the position function $s=s(t)$.

For a), I multiplied $64$ by $5$ and got $320$. But, I'm currently stuck on b); I got $s(t)=-32t^2+c$, but I can't figure out how to calculate the $c$ value, because there is no $s(0)=0$. Thank you!

edited Mar 11 '21 at 19:36

Sebastiano

7,649

asked Mar 11 '21 at 19:25

Julia

It says it is dropped from height of $1000$ ft. – Math Lover Mar 11 '21 at 19:27
s(0) is the height at time t=0. The ball was dropped from 1000 ft, so s(0) = 1000 – spectralblue Mar 11 '21 at 19:28
Thank you! I figured it out – Julia Mar 11 '21 at 19:34
@Julia Remark: Usually a velocity has units, i.e. $\frac{\textrm{miles}}{\textrm{hour}}$ And why have you changed the numbers? – callculus42 Mar 11 '21 at 19:38

Calculating velocity and position with integrals

0 Answers0