- #1

- 197

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- Homework Statement
- Find velocity-time and position-time equation from velocity-position equation(Kinematics).

- Relevant Equations
- ##v=at+v_{0}##

##v^2=v_{0}^2+2a(x-x_{0})##

##x=x_{0}+v_{0}t+\frac 1 2 at^2##

The velocity-position equation of an object that is moving in a straight line is ##v^2-16=4x##. If ##v_{0}<0## find average velocity for ##3<t<5##.

Answer of the book starts with :

We know that :

##v^2-v_{0}^2=2a(x-x_{0})##

##v^2-16=4x##

So ##v_{0}^2=16## => ##v_{0}=-4## and ##a=2##.

##v=at+v_{0}## => ##v=2t-4##

I can't undestand how it finds out that at t=0 we have ##v_{0}=-4## because it might be ##t=t_{0}>0##. In this case book's answer is wrong be cause we should use ##v=a(t-t_{0})+v_{0}## ...

Answer of the book starts with :

We know that :

##v^2-v_{0}^2=2a(x-x_{0})##

##v^2-16=4x##

So ##v_{0}^2=16## => ##v_{0}=-4## and ##a=2##.

##v=at+v_{0}## => ##v=2t-4##

I can't undestand how it finds out that at t=0 we have ##v_{0}=-4## because it might be ##t=t_{0}>0##. In this case book's answer is wrong be cause we should use ##v=a(t-t_{0})+v_{0}## ...