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# When a constant force is applied to a body, it moves with uniform:A. AccelerationB. VelocityC. SpeedD. Momentum

Last updated date: 15th Sep 2024
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Hint: You could easily answer this question with the help of Newton’s second law of motion. You may recall that this law expresses force in terms of the given quantities in its various forms. Thus, you could see that which of these quantities would have been uniform if the force acting on the body was constant.

Formula used:
Newton’s second law,
$F=\dfrac{dp}{dt}$

Complete Step by step solution:
In the question, we are said that a constant force is being applied to a body and we are asked to find which among the given quantities remains uniform in such a condition.

In order to answer this let us recall Newton’s second law of motion, according to which time rate of change of linear momentum gives the force acting on a body. That is,
$F=\dfrac{dp}{dt}$ ……………………………………………. (1)

But we know that momentum is the product of mass and velocity and also for constant mass we get,
$F=m\dfrac{dv}{dt}$ ……………………………………………….. (2)

We know that the time rate of change of velocity is the object’s acceleration. So,
$F=ma$
$\therefore a=\dfrac{F}{m}$

Thus, we see that acceleration is directly proportional to force and inversely proportional to object’s mass. Therefore, we could say that, for uniform force acting on a body of constant mass, acceleration would also uniform.

Hence, option A is found to be the correct answer.

Note:
In case you're wondering about other quantities given in the question: speed, velocity and momentum, let us discuss them. From equation (1) we see that, time rate of change of momentum gives the force. So if the momentum had been uniform or constant, the force would have been zero. Similarly, from equation (2) we could directly conclude that constant velocity would have resulted in zero force on the body.