Question

A 95-kg halfback makes a turn on the football field. The halfback sweeps out a path that is a portion of a circle with a radius of 12-meters. The halfback makes a quarter of a turn around the circle in 2.1 seconds

A) find the velocity of the halfback

B) find the acceleration of the halfback

Answer 1

For part A you need to remember the equation for arc length, because this will give you the distance the halfback travels:

\[a=\theta r\]
Where a is the arc length (the distance traveled in this case), θ is the angle swept through (a quarter of the circle in this case, or π/2), and r is the radius of the circle (12 m).

The velocity is distance over time (2.1 s in this case), so the magnitude of the velocity is given by:

\[v={\theta r \over t}\]
And the direction of the velocity is toward the centre of the circular path.

As with your last question, the acceleration is the centripetal acceleration, which is:

\[a_c={v^2 \over r}\]