Question

A vehicle is moving on a rough road in a straight line with uniform velocity. Then,
A) no force is acting on the vehicle
B) an external force must act on the vehicle
C) an acceleration is being produced in the vehicle
D) no work is being done on the vehicle

Answer 1

Force on an object is defined as the product of acceleration of the object and mass of the object. When a body is moving with uniform velocity, its acceleration is zero and thus, there is no force acting on that body. But when this body is moving on a rough surface, the whole picture changes.

Complete answer:
We know that force acting on an object is the product of acceleration of that object and mass of the object. Mathematically, force is given by
$F=ma$
where
$F$ is the force acting on an object
$m$ is the mass of the object
$a$ is the acceleration of the object
Let this be equation 1.
Let us take the example of a moving car to understand force. The force acting on a moving car is equal to the product of mass of the car and acceleration of the car. To have an acceleration, the vehicle must be having some velocity. We know that acceleration of an object is defined as the change in its velocity, with respect to time. It is given by
$a=\dfrac{dv}{dt}$
where
$a$ is the acceleration of an object
$dv$ is the change in velocity during a time interval $dt$
Let this be equation 2.
Now, suppose that the car is moving with a uniform velocity. There is no change in velocity with respect to time and hence, acceleration of the car turns out to be zero, as given below
$a=\dfrac{dv}{dt}=\dfrac{0}{dt}=0$
Let this be equation 3.
Therefore, force acting on a moving car with uniform velocity is equal to zero. Here, we have considered that the surface on which the car is moving is smooth, and hence, there is no frictional force acting on the moving car. But what if the surface is rough?
When the car is moving on a rough surface, a force of friction acts on the car. Force of friction or frictional force refers to the force acting between two surfaces in contact. Since the tyres of the moving car are in contact with the rough surface, a frictional force comes into play between the two surfaces, in addition to the force of the moving car.
Frictional force on an object is dependent on the texture of the surface on which the object is in contact. Frictional force is also dependent on the position of the object with respect to the surface. If the object is resting on a surface, the frictional force acting on the object is equal to the weight of the object. But if the object is moving, as in the case of a moving car, the frictional force on the moving car increases and is more than the weight of the car.
Therefore, when a car is moving with uniform velocity on a rough surface, frictional force acts on the car

Hence, option B is the correct answer.

Additional information:
Since the car is moving with uniform velocity, the acceleration of the car is equal to zero, as already mentioned. Work done on the moving car is equal to the work done by the frictional force on the car. The moving car keeps getting vertically displaced frequently while moving on the rough surface and the work done on the moving car is equal to the product of frictional force and vertical displacement of the car.

Note:
Students should not get confused with option A. In the first option, it is said that no force is acting on a moving car with uniform velocity. This would have been true if the car was not moving on a rough surface. For reference, students can go back to equation 3. But since the car with uniform velocity is moving on a rough surface, a frictional force or an external force comes into play.