What Is the Magnitude of the Particle's Acceleration When Velocity Is Zero?

[Ammar w]

Homework Statement

A particle moving along the x-axis has a position given by
x = 24t - 2.0t³ m, where t is
measured in s. What is the magnitude of the acceleration of the particle at the instant
when its velocity is zero?

Homework Equations

v=dx/dt

a=dv/dt=d²x/dt²

The Attempt at a Solution

v = dx/dt = 24 - 6t² = 0 =>t² = 4 => t= ± 2

a = dv/dt = d²x/dt² = -12t

=> a = -12 (2) = -24 m/s²

or a = -12(-2) = 24 m/s²

----------
the right answer is a = 24 m/s²
but why??

 

[PhanthomJay]

Time cannot be negative so your second solution, although meaningful in a mathematical sense, can be discarded. But this observation not withstanding, the problem asks for the magnitude of the acceleration.

 

[Ammar w]

Time cannot be negative so your second solution, although meaningful in a mathematical sense, can be discarded. But this observation not withstanding, the problem asks for the magnitude of the acceleration.

Yes, that's it.
Thank you.
the magnitude is 24 whether time = 2 or -2.