SOLUTION: Hi all, thanks for all your help so far; ive almost gotten through my vectors stuff, but I need help with the following question: A particle with mass m = 2.5 is moving along a st

Question 205740: Hi all, thanks for all your help so far; ive almost gotten through my vectors stuff, but I need help with the following question:
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.
I know its a little long, I cant seem to make sense of it thouh, so any help will be awesome.
Thnaks, -Nick.
Found 2 solutions by nerdybill, amalm06:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
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...
Answer by amalm06(224) (Show Source): You can put this solution on YOUR website!
(Position function)
(Instantaneous velocity at any time t)
(Kinetic energy of particle)
=
=
= (Answer)
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