Finding Velocity of Particle: Problem Solved

[tennistudof09]

I wanted to make sure I did this problem correctly. The problem is:

A particle moves along a straight line and its position at time t is given by s(t)=2t^3 - 21t^2 + 60t where s is measured in feet and t in seconds.

Find the velocity of the particle when t=0.

I took the derivative of s(t) and got 6t^2 - 42t + 60, and then substituted 0 in for t. I got 60ft/sec for the answer. Is this correct??

 

[bblenyesi]

$$\frac{ds}{dt}=v(t)$$

$$\frac{dv}{dt}=a(t)$$

Where $$s(t)$$ is the displacement vector, $$v(t)$$ is the velocity vector and
$$a(t)$$ is the acceleration vector.

If you look at it in any given point, so I'm guessing that it's correct.