Starting from rest, a particle is constrained to move in a circle of radius #4 m#. The tangential acceleration is #a_t = 9 m/s^2#. How long will it take to rotate #45º#?

1 Answer
Mar 1, 2017

Answer:

#t = sqrt((2 pi)/9) "seconds" #

Explanation:

If you think of this as a linear problem, the magnitude of the velocity will simply be:
#|v| = |v_0| +|a*t|#
And the other equations of motion work in a similar way:
#d = v_0*t + 1/2 a*t^2#

The distance along the direction of travel is simply one eighth of a circle:
#d = 2 pi*r/8 = 2 pi * 4/8 = pi " meters"#

Replacing this value in the equation of motion for distance gives:
#pi = v_0*t + 1/2 a*t^2#
#pi = 0*t + 1/2 a*t^2#
#2 pi = a*t^2#
#2 pi = 9 * t^2#
#(2 pi)/9 = t^2#
#sqrt((2 pi)/9) = t#