A girl jogs around a horizontal circle with a constant speed.She travels one fourth of a revolution, a distance of 25 m along the circumference of the circle, in 5.0 s.The magnitude of her acceleration is: A)0.31 m/s² B)1.3 m/s² C)1.6 m/s² D)3.9 m/s² E)6.3 m/s²

Question

Quizplus · Accepted Answer

First, we need to find the speed of the jogger. 
Speed = Distance/Time 
Speed = 25 m / 5 s 
Speed = 5 m/s

Next, we can find the circumference of the circle by multiplying the distance traveled by 4: 
Circumference = 25 m x 4 
Circumference = 100 m

Using the formula for centripetal acceleration: 
a = v^2 / r

We can rearrange the formula to solve for radius: 
r = v^2 / a

Plugging in the known values: 
r = (5 m/s)^2 / a 
r = 25 m^2 / a

We know that one fourth of the circumference is covered in 5 seconds, so we can set up the equation: 
(1/4) x 100 m = 25 m = distance traveled 
We also know that distance = circumference x fraction of circle traveled, so: 
25 m = (2πr / 4) 
25 m = πr / 2 
r = 50 m / π

Plugging this value of r into our earlier equation: 
50 m / π = 25 m^2 / a 
a = (25 m^2) / (50 m / π) 
a = 1.6 m/s^2

Therefore, the magnitude of her acceleration is 1.6 m/s^2.

A Girl Jogs Around a Horizontal Circle with a Constant