Motion equation of object is x = 15 - 12t + 3 {t}^(2) How long did it move until it stops? (I think it is projectile motion, I'm not sure.) A) 5 sec B) 0,3 sec C) 0,4 sec D…

Question

Motion equation of object is


`x = 15 - 12t + 3 {t}^(2)`
How long did it move until it stops?
(I think it is projectile motion, I'm not sure.)

A) 5 sec
B) 0,3 sec
C) 0,4 sec
D) 4 sec
E) 2 sec

Answer 1

Take the derivative to find the velocity of the object:

`v=(\mathrm dx)/(\mathrm dt)=-12+6t`

The object stops when
`v=0`:

`-12+6t=0\implies6t=12\implies t=2`

so the answer is E.