NOTE: The graph has been uploaded as a photo. I don\'t know why it\'s crooked. I

Question

NOTE: The graph has been uploaded as a photo. I don't know why it's crooked. I tried to fix it, but it uploads sideways into Chegg. Also, the lines on the graph shouldn't be there. They should be three separate lines: one going up, the other straight across, and the final line at the end of the graph.

At t = 0s an object of mass 0.50 kg is passing through x = 0m with a velocity of some unknown value in the positive x-direction. It is then subjected to a net force in the x-direction that varies in magnitude and direction as shown by the graph.

The graph shows the force as a function of time

When the force is positive it means the force is directed in the +x direction. When the force is negative it is directed in the -x direction.

(a) We observe the object's velcoity at t= +4.0s is 20.0 m/s in the positive x direction. What was the speed of the object at t = 0s?

(b) When is the first time the object reveres direction?

(c) When is the second time the object reverses direction?

(d) What is the object's kinetic energy at t = 6.0s?

(e) At what time, between t = 0s and t = 8.0s, is the kinetic energy largest?

The graph has been uploaded as a photo. I don't know why it's crooked. I tried to fix it, but it uploads sideways into Chegg. Also, the lines on the graph shouldn't be there. They should be three separate lines: one going up, the other straight across, and the final line at the end of the graph. At t = 0s an object of mass 0.50 kg is passing through x = 0m with a velocity of some unknown value in the positive x-direction. It is then subjected to a net force in the x-direction that varies in magnitude and direction as shown by the graph. The graph shows the force as a function of time When the force is positive it means the force is directed in the +x direction. When the force is negative it is directed in the -x direction. We observe the object's velcoity at t= +4.0s is 20.0 m/s in the positive x direction. What was the speed of the object at t = 0s? When is the first time the object reveres direction? When is the second time the object reverses direction? What is the object's kinetic energy at t = 6.0s? At what time, between t = 0s and t = 8.0s, is the kinetic energy largest?

Explanation / Answer

a) itnegral of F dt = m dv

20*2/2 -20*2 = 0.5*(20-v)

v=60 m/s

b) reverse directions when v = 0

so integral of f dt = 0.5*-60

20*2/2 -20*(t-2) = 0.5*-60

t= 4.5 s

c) will be when v = 0 again
so net impulse after 4.5 s is zero

so since 1.5 s left with -20 N

then 1.5 s with 20 N is needed

so 6+1.5 = 7.5 s

d) largest when v is largest

two possibilities t=2 and t = 6

at t=2 would be

20*2/2 = 0.5*(v-60)

v=100 m/s

at t=6

-20*1.5 = 0.5*v
v=-60

so largest at t=2

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