The car travels around the portion of a circular track having a radius of r = 500 ft such that when it is at point A it has a velocity of 4 ft/s , which is increasing at the rate of v˙=(0.004t)ft/s2, where t is in seconds. A-Determine the magnitude of the velocity when it has traveled three-fourths the way around the track. B-Determine the magnitude of the acceleration when it has traveled three-fourths the way around the track.

Explanation:

Given

velocity at A is

For

velocity is increasing at

Tangential acceleration is given by

at

thus

Velocity in terms of Displacement is given by

When car has traveled th of distance i.e.

on solving we get

Thus velocity at

(b)Acceleration when car has traveled three-fourth the way of track

normal acceleration

Tangential acceleration

Net acceleration

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