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A ball rolling down a hill is accelerated at 3.6 m/s^2. What is the time taken by the...

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lxsptter | Student, Undergraduate | Valedictorian

Posted March 25, 2012 at 2:47 PM via web

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A ball rolling down a hill is accelerated at 3.6 m/s^2. What is the time taken by the ball to travel 400 m.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted March 25, 2012 at 2:54 PM (Answer #1)

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The ball rolling down a hill is accelerated at 3.6 m/s^2. The time required by the ball to travel 400 m has to be determined. It is assumed that the ball starts from rest.

For an object starting with an initial velocity u and traveling for a duration of time t while it is being accelerated at a rate of acceleration equal to a, the distance covered is equal to d = u*t + (1/2)*a*t^2.

Here, the initial velocity is 0. The acceleration is a constant value of 3.6 m/s^2 and the distance covered is 400 m. The time take by the ball to cover the distance is t such that 400 = 0*t + (1/2)*3.6*t^2

=> t^2 = 400*2/3.6

=> t^2 = 2000/9

=> t = 14.90 s

The ball covers the 400 m in a duration of time equal to 14.0 s.

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