A force is applied to a 5.0-kg radio-controlled model car parallel to the x -axi

Question

A force is applied to a 5.0-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 F  is the net force acting on it.

Part A

Use the work-energy theorem to find the speed of the car at x=3.0m

Part B

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

Part C

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

Explanation / Answer

here,

mass , m = 5 kg

A)

at x = 3 m

for F vs x graph , the area under the curve is work done

let the final speed be v

using work energy theorm

work done = kinetic energy gained

0.5 * 2 * 2 + 1*2 = 0.5 * 5 * v^2

v = 1.26 m/s

B)

at x = 4 m

the work done is same

so the speed is also same

C)

at x = 7 m
  
let the final speed be v

using work energy theorm

work done = kinetic energy gained

0.5 * 2 * 2 + 1*2 - 0.5 * 1 * 2 = 0.5 * 5 * v^2

v = 1.1 m/s

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