Thepositionofaparticlemovingalongthexaxis...Thepositionofaparticlemovingalongthexaxisisgivenbyx=6.0t^2−1.0t^3,wherexisinmetersandtinseconds.Whatisthepositionoftheparticlewhenitsaccelerationiszero?

Question

The position of a particle moving along the x axis...
The position of a particle moving along the x axis is given by x = 6.0 t^2 − 1.0 t^3, where x is in meters and tin seconds. What is the position of the particle when its acceleration is zero?
A.24m
B.12m
C.32m
D.16m
E.2.0m
Please help!

Answer 1

v=dx/dt=2(6.0)t+3(1)t^2 =12t-3t^2
a=dv/dt=12-6t
Now,the question need you to find out the position of the particle when its acceleration is zero.
Hence,
if a=0,
0=12-6t
t=2s
Then,you need to substitute t=2s into the original equation x = 6.0 t^2 − 1.0 t^3.
x=6.0(2^2)-1.0(2^3) =24-8 =16m
Hence,when the position is 16m,the acceleration will be 0
the answer you can find out is D