A 4.40-kg object is constrained to move along a straight line. Its initial speed

Question

A 4.40-kg object is constrained to move along a straight line. Its initial speed is 12.0 m/s in one direction, and its final speed is 8.00 m/s in the opposite direction. Complete the graph of force versus time with appropriate values for both variables in the figure below. Assume each tick mark on the time axis is 1 s. 1) What is the time t_1. (Express your answer as integer.) s 2) Calculate the value for F_1. (Express your answer to three significant figures.) 3) Calculate the value for F_2 (Express your answer to three significant figures.) N 4) Calculate the value for. (Express your answer to three significant figures.) N

Explanation / Answer

Here ,

vi = 12 m/s

vf = -8 m/s

mass m = 4.4 Kg

a) the time tf is

tf = 8 s

the time tf is 8 s

b)
let the each tick on the y axis is a

Now , for the change in momentum

change in momentum = area under the Force-time curve

4.4 * (vf - vi) = - 0.5 * 4a * 4 + a * 0.5 * 2 - 2 * a * 0.5 * 2

4.4 * (-8 - 12) = - 0.5 * 4a * 4 + a * 0.5 * 2 - 2 * a * 0.5 * 2

solving for a

a = 9.78 N

Hence , F1 = -4 a

F1 = -4 * 9.78

F1 = -39.12 N

c)

F2 = -2 a

F2 = -2 * 9.78

F2 = -19.6 N

d)

F3 = a

F3 = 9.78 N

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