# Thread: Derivatives: Velocity + Acceleration

1. ## Derivatives: Velocity + Acceleration

The equation of motion of a particle, where s is in meters and t is in seconds, is given by the equation below.

$\displaystyle s = 5t^3 - 4t$

i know that

$\displaystyle v(t) = 15t^2 - 4$
and
$\displaystyle a(t) = 30t$

The question is "Find the acceleration when the velocity is 0. (Round the answer to one decimal place.)"

I feel dumb asking this cause it seems like an easy problem, but i have no clue what the answer is.

2. Originally Posted by break
The equation of motion of a particle, where s is in meters and t is in seconds, is given by the equation below.

$\displaystyle s = 5t^3 - 4t$

i know that

$\displaystyle v(t) = 15t^2 - 4$
and
$\displaystyle a(t) = 30t$

The question is "Find the acceleration when the velocity is 0. (Round the answer to one decimal place.)"

I feel dumb asking this cause it seems like an easy problem, but i have no clue what the answer is.
Just set the velocity equal to zero and solve the quadratic for t.

$\displaystyle 15t^2-4=0$

Just solve that equation for t, and then plug that into $\displaystyle a(t)$ to obtain the acceleration.

$\displaystyle 15t^2=4$

t=$\displaystyle \frac{2}{\sqrt{15}}$

It's conventional to rationalize the denominator. So t could be written as $\displaystyle \frac{2\sqrt{15}}{15}$

$\displaystyle a(\frac{2\sqrt{15}}{15})=30(\frac{2\sqrt{15}}{15}) =4\sqrt{15}$