FOR THE FOLLOWING QUESTIONS, I HAVE THE ANSWERS BUT DON\'T KNOW HOW TO ARRIVE AT

Question

FOR THE FOLLOWING QUESTIONS, I HAVE THE ANSWERS BUT DON'T KNOW HOW TO ARRIVE AT THE SOLUTION-- SO PLEASE SHOW DETAILED WORK TO HELP OUT. THANKS!

A ball is rolled up an incline with an initial velocity v0.

During the last second of its motion, the ball
travels 2 m, and at the top of the incline its speed is vf = 1 m/s.

During the whole motion up the incline, the ball slows down because it has a constant acceleration.

(a) Find the magnitude of the acceleration of the ball.

a=-2m/s2

(b) Find the speed of the ball one second before it reaches the end of the incline.

v=3m/s

(c) If the initial speed is v0 = 7 m/s, how long does it take for the ball to travel from the bottom to
the top of the incline?

t=3s

(d) How long is the incline?

   12m

Explanation / Answer

a) magnitude of acceleration Vt = Vo + a * t (t = 1 because "During the last second of its motion") Vt = Vo + a * t 1 = Vo + a * 1 Vo = 1 - a S = vo * t + 0.5 * a * t^2 2 = (1 - a) * 1 + 0.5 * a * 1^2 2 = 1 - a + 0.5 a 1 = 0.5 a a = 2 m/s b) speed of the ball one second before it reaches the end of the incline. same as Vo for the last second of its motion V = Vo = 1 - a V = 1 - (-2) V = 3 m/s c) how long does it take for the ball to travel from the bottom to the top of the incline Vt = Vo + a * t 1 = 7 + (-2) * t 1 = 7 - 2t 2t = 6 t = 3s d) the incline = the distance from the bottom to the end s = Vo * t + 0.5 * a * t^2 s = 7 * 3 + 0.5 * (-2) * 3^2 s = 21 - 9 s = 12 m

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