A car is driven from rest on a long straight road. The car engine exerts a constant driving force.
The diagram shows the horizontal forces acting on the car. The resistive forces are proportional to the speed of the car.
Why does the car eventually reach a maximum speed?
Correct Answer: \( \boxed{\mathrm{D}} \)
The resultant force acting on the car is:
\( F_{\mathrm{resultant}} = F_{\mathrm{driving}} – F_{\mathrm{resistive}} \)
Initially, the car is at rest, so the resistive forces are small and the driving force is greater than the resistive force.
Therefore, there is a resultant forward force and the car accelerates.
As the speed increases, the resistive forces increase because they are proportional to the speed of the car.
The increasing resistive forces reduce the resultant force and therefore reduce the acceleration.
Eventually, \( F_{\mathrm{driving}} = F_{\mathrm{resistive}} \).
At this point:
\( F_{\mathrm{resultant}} = 0 \)
and from Newton’s Second Law:
\( a = \frac{F_{\mathrm{resultant}}}{m} = 0 \)
The car then continues at a constant maximum speed, often called the terminal speed.
Therefore, the resistive forces increase until the acceleration becomes zero.
Hence, the correct answer is (D).
A mattress placed on a bed contains many compression springs.
Which energy store of the mattress increases when a person lies on the bed?
Correct Answer: \( \boxed{\mathrm{C}} \)
When a person lies on the bed, their weight compresses the springs inside the mattress.
Work is done in deforming the springs, and this energy is stored as elastic potential energy.
The elastic energy stored in a spring is given by:
\( E_{\mathrm{e}}=\frac{1}{2}kx^{2} \)
where \(k\) is the spring constant and \(x\) is the compression of the spring.
As the springs are compressed, the value of \(x\) increases, so the elastic energy store increases.
The mattress remains stationary, so its kinetic energy does not increase. No chemical reaction occurs, and the gravitational potential energy of the mattress itself does not increase.
Therefore, the energy store that increases is the elastic energy store.
Hence, the correct answer is (C).
Which property of an object never changes when a force acts on the object?
Correct Answer: \( \boxed{\mathrm{A}} \)
A force can change the motion or shape of an object.
According to Newton’s Second Law:
\( F = ma \)
A resultant force can produce acceleration, which may change the speed or direction of motion of an object.
Forces can also stretch, compress, bend, or deform objects, causing changes in their size or shape.
However, applying a force does not change the amount of matter contained in the object.
Mass is an intrinsic property of the object and remains constant when a force acts on it.
Therefore, among the given options, mass is the property that never changes due to the action of a force.
Hence, the correct answer is (A).
