Question

a certain light truck can go around a flat curve having a radius of 150m with a maximum speed of 32.0m/s^2 . With what maximum speed can it go around a curve having a radius of 75.0m?

Answer 1

Use
\[v=\frac{2\pi r}{T}\]
\[T=\frac{2\pi r}{v}\]
--------------------------------------
For radius 150m,
\[T=\frac{2\pi (150)}{32}\]
\[T=29.4s\]
--------------------------------------
For radius 75m,
\[v=\frac{2\pi r}{T}\]
\[v=\frac{2\pi (75)}{29.4}\]
\[v=?\]

Answer 2

Hm... this is a centripetal acceleration/force problem.
The equation for centripetal acceleration for a particle traveling a circular path is:
a=v²/r.
Since you're given the values of the equation on the right for first set of conditions, a = 6.83m/s².
Solve the equation for v with the second set of conditions to yield v = sqrt(a*r)=sqrt(6.83*75)=22.6m/s.

By the way, you wrote that the maximum speed is "32m/s²", when in fact speed is given in m/s.