a car travels 67.5 degrees of the way around a circle of radius 16.2m in a time

Question

a car travels 67.5 degrees of the way around a circle of radius 16.2m in a time of 8.65 at a constant speed. The initial velocity is west. What is the magnitude of the average acceleration of the car during this turn? a car travels 67.5 degrees of the way around a circle of radius 16.2m in a time of 8.65 at a constant speed. The initial velocity is west. What is the magnitude of the average acceleration of the car during this turn? a car travels 67.5 degrees of the way around a circle of radius 16.2m in a time of 8.65 at a constant speed. The initial velocity is west. What is the magnitude of the average acceleration of the car during this turn?

Explanation / Answer

speed of the car , v = theta * 2*pi*r/(t*360)

v = 67.5 * 2*pi*16.2/(360 * 8.65)

v = 2.21 m/s

initial velocity , u = -2.21 i m/s

fianl velocity , v = 2.21 *(-cos(67.5) i -j * sin(67.5))

v = -0.846 i - 2.04 j m/s

Now , magnitude of acceleration = ( -0.846 i - 2.04 j + 2.21 i )/8.65

magnitude of acceleration = 0.284 m/s^2

the magnitude of average acceleration of the car is 0.284 m/s^2

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