# Linear velocity equation for a object trown vertically up

1. Sep 10, 2015

### bjornove

The problem statement, all variables and given/known data
The velocity of an object thrown vertically up in the air is given by V(t)=64-32t
a) What is the average velocity during the first second?
b) What is the average velocity between t=1 and t=3?

The attempt at a solution
a) displacement X1-X0 is given by the integral of v(t)dt between t=0 and t=1
solving integral gives 64t-16t^2. Entering time intevall between t=0 and t=1 give a displacement of 48m
That is: average velocity is 48m/s the first second
b) entering time bewteeen t=1 and t=3 gives dispplacement 192-144-(64-16)= 0
That is: average velocity is 0. This make sense since the curve x(t) is a parabole and t=2 give maximum height and velocity before that is positiv and after that is negative and so it cancels out

Is this way of thinking correct?. I am a teacher (biology, not physics) and I am trying to help a friend with this problem. One more thing I am thinking about. The velocity equation is linear here. Is this realistic when throwing a object up in the air? It seem strange that this is linear. Wouldn't velocity varies in such a scenario?

2. Sep 10, 2015

### BvU

Hello Bjorn, welcome to PF (which also has a biology section...) !

Absolutely correct.

And linear in time doesn't mean fixed. linear in time means the graph of v versus t is a straight line with fixed slope. That constant slope is called the acceleration: change in velocity/unit of time. Graviational acceleration of the face of the earth is generally written "g", with confusion about the sign from time to time . Your object must be on a strange planet to experience an acceleration of -64 m/s2 ...