7. You are running around a curve on a track in lane that has a radius of 10 m a

Question

7. You are running around a curve on a track in lane that has a radius of 10 m and you are running at a constant speed of 9 m/s.

7.a. What are your centripetal and tangential accelerations?

7.b. You move out to a lane that has a radius of 15m, still maintaining a constant speed of 9 m/s. It takes you 1.5 seconds to change lanes. What is the average angular acceleration of an imaginary line between you and the center of the track during this time?

7.c. You continue run at 9 m/s in the lane with radius 15 m. Now that you have established your new lane, what are your centripetal and tangential accelerations?

Explanation / Answer

7.

Centripetal acceleration is a = V2/r

a = 92/10 = 8.1 m/s2

Tangential acceleraion is ZERO

7b.

Average angular acceleration is w2-w1/t2-t1

w is angular velocity

w =v/r

Average angular acceleration is ((v/r2)-(v/r1))/1.5 seconds

r1 =10m

r2 =15m

7c.

centripetal acceleration is a =v2/r

a= 92/15 = 81/15 = 5.4 m/s2

Tangential acceleration is ZERO.

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