A motorcycle starting at the origin O moves along a circular road of radius 50 m

Question

A motorcycle starting at the origin O moves along a circular road of radius 50 m at a constant speed of 2 m/s. Initially, the motorcycle's velocity points North (the j direction). After traveling a quarter circle, the motorcycle reaches point A, and its velocity now points East (the i direction). (a) What is the travel time (in s) from O to A? (b) What is the average velocity (in m/s) for the trip from O to A? Express your answer in terms of the unit vectors i and j. (c) What is the average acceleration (in m/s') for the trip from O to A? Express your answer in terms ofthe unit vectors i and j.

Explanation / Answer

a)The distance covered in travelling quarter circle is:

d = 2 pi R/4 = pi R/2 = 3.14 x 50/2 = 78.5 m

t = d/v = 78.5/2 = 39.25 s

Hence, t = 39.25 s

b)the average velocity will be:

Aav = 0i + 0j

c)a = v^2/R = 4/50 = 0.08 m/s^2

Hence, a = 0.08 i + 0.08 j

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