Question

A particle moves along a straight line with equation of motion s=f(t), where s is measured in meters and t in seconds. Find the velocity and speed when t=2. f(t)=90+20t-4.5t^2

Answer 1

Sorry, that was incomplete. Rewriting it.

Answer 2

To solve s = f(t), the first thing we have to do is find out what f(t) is. Since t = 2, what we do is replace every t in the equation with a 2.

f(t) = 90 + 20t - 4.5t^2.
f(2) = 90 + 20(2) - 4.5(2)^2

It's pretty simple from here:

f(2) = 90 + 40 - 4.5(4)
f(2) = 90+ 40 - 18
f(2) = 112.

Now we know s = 112. So we have 112 metres and 2 seconds. The formula for velocity is distance / time, so our velocity = 112 / 2. 112/2 = 56, so our velocity is 56 metres per second, or 56 m/s.