# Physics Questions and Answers – Work-Energy Theorem for a Variable Force

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This set of Physics Questions & Answers for Exams focuses on “Work-Energy Theorem for a Variable Force”.

1. For a body moving from position Xa to position Xb under a variable force, what is the work done?
a) W = F * (X2 – X1)
b) -W = F * (X2 – X1)
c) W = -F * (X2 – X1)
d) W = F * (X1 – X2)

Explanation: Kinetic energy (K) = 1/2 x m x v2
dK/dt = m*v*dv/dt
Force (F) = m*a
= m*dv/dt
dK/dt = F*v
= m*v*dv/dt
$$\int_{K1}^{K2}$$ dK/dt = $$\int_{Xa}^{Xb}$$ F * dX/dt
$$\int_{K1}^{K2}$$ dK = $$\int_{Xa}^{Xb}$$ F * dX
K2 – K1 = F (X2 – X1)
W = F * (X2 – X1).

2. The work-energy theorem is valid only for positive work done.
a) True
b) False

Explanation: Work energy theorem holds for both positive and negative work done. If the work doneis positive then final kinetic energy increases by the amount of the work and if work done is negative then final kinetic energy decreases by the amount of work done.

3. A car having a mass of 1 metric ton is moving with a speed of 30 m/s. It suddenly applies the brakes and skids to rest in a certain distance d. The frictional force between the tyres and road is 6000 N. What is the value of d?
a) 25 m
b) 50 m
c) 75 m
d) 100 m

Explanation: Let; m = 1000 kg
From Work-Energy theorem
Kf – Ki = F * d
0 – (1/2 * m * v2) = -6000 * d
1/2 x 1000 x 302 = 6000 x d
d = 75 m.

4. For the graph shown in the figure, what is the difference between x-coordinate of A and B called?

a) Internal pressure
b) External pressure
c) Work
d) Power

Explanation: The difference between x-coordinate of A and B can be written as “Kb – Ka”. This is the difference between kinetic energies at two positions. This gives us the “work done”.

5. For the graph shown in the figure, what is the area under the curve AB called?

a) Force applied
b) Displacement
c) Work
d) Power

Explanation: The area under the curve is a summation of the product of x-coordinate and y-coordinate at every point under the curve.
That is; “F * x”.
F * x = Work done.
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6. A “variable force” is the force that only increases with time.
a) True
b) False

Explanation: A “variable force” is the force that changes with time. This force can increase or decrease at random time intervals. However, it is not constant with respect to time.
i.e., dF/dt is not equal to “zero”.

Sanfoundry Global Education & Learning Series – Physics – Class 11.