Question

QUESTION 1

Towards the end of a race, two runners are separated by a distance 34 m. The first runner is closest to the finish line and the second runner is farther from the finish line than the first runner. The first runner is running a constant 4.4 m/s and the second runner is running a constant 5.8 m/s. If the two runners get to the finish line at the same time, how long (in s) did it take the two runners to get to the finish line?

QUESTION 2

An object is moving around a circle with a radius of 0.3 m. The object starts from rest and then experiences a constant angular acceleration. The tangential velocity of the object increases from 2 m/s to a final velocity v m/s over 6 s. If the magnitude of the angular acceleration is 0.9 in rad/s², what is the value of the final velocity v (in m/s)?

Answer 1

(1) To get to the finish line at the same time, say, after t seconds, the second runner has to cover 34 m more than the distance covered by the first one.

Now, at 4.4 m / s, the first runner will cover 4.4t m in time t seconds,

and, at 5.8 m / s, the second runner will cover 5.8t m in time t seconds.

Hence, 5.8t - 4.4t = 34

or, 1.4t = 34

or, t = 34 / 1.4 ~ 24.3.

Hence, it took 24.3 seconds for the two runners to get to the finish line at the same time.

(2) Tangential acceleration ( a ) = Angular acceleration x Radius of circular motion,

or, a = 0.9 rad/s² x 0.3 m = 0.27 m / s².

Now, time taken to reach at the final velocity v m / s from an initial velocity u = 2 m / s is t = 6 s.

Hence, v = u + at = 2 m / s + 0.27 m / s² x 6 s

or, v = 3.62 m / s.