Unit 5 - Part 2 Centripetal acceleration Assessment POSSIBLE POIN VTS: 6.67 What is the centripetal acceleration of an object that is moving around a curve with a radius of 8 m if it completes 4 revolutions in 20 seconds?Hint: Find Period, then use that to find Velocity, then use that to find Acceleration. 0.63m/s2 3.63m/s2 12.63m/s2 30.63m/s2

To find the centripetal acceleration of an object moving around a curve, we can follow these steps:<br /><br />1. Find the period (T) of the motion:<br /> The period is the time it takes for the object to complete one revolution. In this case, the object completes 4 revolutions in 20 seconds, so the period is:<br /> T = 20 seconds / 4 revolutions = 5 seconds per revolution<br /><br />2. Find the velocity (v) of the object:<br /> The velocity can be calculated using the formula:<br /> v = 2πr/T<br /> where r is the radius of the curve and T is the period.<br /> v = 2π * 8 m / 5 s = 8π m/s<br /><br />3. Find the centripetal acceleration (a_c):<br /> The centripetal acceleration can be calculated using the formula:<br /> a_c = v^2 / r<br /> where v is the velocity and r is the radius of the curve.<br /> a_c = (8π m/s)^2 / 8 m = 8π^2 m/s^2 ≈ 63.66 m/s^2<br /><br />Therefore, the centripetal acceleration of the object is approximately 63.66 m/s^2, which is closest to the option $12.63m/s2$.