The velocity v(t) of a ball thrown upward satisfies the equation v(t) = v_() + a

Question

The velocity v(t) of a ball thrown upward satisfies the equation v(t) = v_() + at, where v_() is the initial velocity of the ball in ft/s and a is the acceleration in ft/s^2. Given the data in Fig. P1.6, find the equation of the line representing the velocity v(t) of the ball, and determine both the initial velocity v_() and the acceleration a. Sketch the graph of the line v(t), and clearly indicate both the initial velocity and the acceleration on your graph. Also determine the time at which the velocity is zero.

Explanation / Answer

We have given v(t) = v0+at

and at time t = 1 sec, the velocity v(t) = 67.8 ft/s

hence v(1) = 67.8 = v0 + a*1....................(1)

and at time t = 3.0 sec, the velocity v(t) = 3.4 ft/s

hence v(3) = 3.4 = v0 + a*3....................(2)

by solving the equation (1) and (2)

2a = 64.4

a = 32.2 ft/s2 ........................Ans.

by putting the value of a in eq. (1)

we get v0 = 67.8 - 32.2 = 35.6 ft/s ............Ans.

hence equation of motion is

v(t) = 35.6 + 32.2*t    .....................Ans.

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