A particle with mass m 25 is moving along a straight trajec

A particle with mass m = 2.5 is moving along a straight trajectory. The distance covered by a particle is described by the function S(t) = t^3 + 2t^2 where t>0 is the time.
a) Kinetic Energy E of a particle is given by E = mv^2/2, where v is the particle speed. Find a function that describes the kinetic energy of this particle.

Solution

Since
S(t) = t^3 + 2t^2
describes the distance
then the derivative is the speed:
S\'(t) = 3t^2 + 4t
.
Now, we can plug it into:
E = mv^2/2
E = (2.4)(3t^2 + 4t)^2/2
You can expand the above...