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A ball starting from rest accelerates uniformly at 5.0 meters per second2 as it rolls 40. meters down an incline. How much time is required for the ball to roll the 40. meters

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nuhulawal20

The time required for the ball to roll down the given distance is 4 seconds.

Given the data in the question;

Since the ball started from rest,

  • Initial velocity; [tex]u = 0[/tex]
  • Acceleration; [tex]a = 5.0m/s^2[/tex]
  • Distance traveled; [tex]s = 40m[/tex]
  • Time taken; [tex]t =\ ?[/tex]

To determine the time required for the ball to travel the given distance, we use the Second Equation of Motion:

[tex]s = ut + \frac{1}{2}at^2[/tex]

Where s is distance traveled, u is initial velocity, a is acceleration and t is time taken.

We substitute our given values into the equation and solve for "t"

[tex]40m = [ 0*t ] + [ \frac{1}{2}\ *\ 5.0m/s^2\ *\ t^2 ]\\\\40m = 2.5m/s^2\ *\ t^2\\\\t^2 = \frac{40m}{2.5m/s^2}\\\\t^2 = 16s^2\\\\t = \sqrt{16s^2}\\\\t = 4s[/tex]

Therefore, the time required for the ball to roll down the given distance is 4 seconds.

Learn more: https://brainly.com/question/3391840

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