A force is applied to a 5.0-\\(\ m kg\\) radio-controlled model car parallel to

Question

A force is applied to a 5.0-( m kg) radio-controlled model car parallel to the (x)-axis as it moves along a straight track. The (x)-component of the force varies with the (x)-coordinate of the car as shown in figure (Figure 1) .Suppose the model car is initially at rest at (x)=0 and (ec F) is the net force acting on it.

a)

Use the work-energy theorem to find the speed of the car at (x)=3.0({ m{ m}}).

b)

Use the work-energy theorem to find the speed of the car at (x)=4.0({ m{ m}}).

c)

Use the work-energy theorem to find the speed of the car at (x)=7.0({ m{ m}}).

Explanation / Answer

w=f.x=1/2mV^2
angel between f and x is 0.
f is 5 part
f=x 0<x<2
f=2 2<x<3
f=0 3<x<4
f=-1/2x+2 4<x<6
f=0 6<x<7

when x multiplied to f and intgration, we get work
dw1=f.dx=x 0<x<2
dw2=f.dx=2 2<x<3
dw3=f.dx=0 3<x<4
dw4=f.dx=-1/2x+2 4<x<6
dw5=f.dx=0 6<x<7

A) if x=3, w=w1+w2=2+2=4
4=1/2*5*v^2
v=1.26 m/s

B) if x=4, w=w1+w2+w3=4
4=1/2*5*v^2
v=1.26 m/s
v(x=3)=v(x=4)=========> we have'nt force


C) if x=7 w=w1+w2+w3+w5+w6 =2+2+0-1+0=3
3=1/2*5*v^2
v=1.1 m/s

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