Question

The motion of a particle is defined by the relation x = 1.5t^4 - 30t^2 + 5t + 10, where x and t are expressed in meters and seconds, respectively. Determine the position, the velocity, and the acceleration of the particle when t = 4 s.

Answer 1

Velocity is:
\[v=\frac{dx}{dt}\]
and
Accleration is:
\[a=\frac{dv}{dx}\]

So basically what you have to do is differentiate that equation twice, and substitude t=4 for x,v,a.

To help you check your calcuations:
\[v=6x^{3}-60t+5\]\[a=18x^{2}-60\]