Question

The kinetic energy of a particle continuously increases with time. We can conclude that:
A. The resultant force on the particle must be parallel to the velocity at all instants.
B. The resultant force on the particle must be at an angle less than$90^\circ$all the time.
C. Its height above the ground level must continuously decrease.
D. The magnitude of its linear momentum is increasing continuously.

Answer 1

Kinetic energy is defined as the ability to do work under motion. Work done by the net force in displacing a particle is equal to the change in its kinetic energy. Kinetic energy is directly proportional to the velocity acting on the particle; this means that the acceleration is also continuously increasing.

Complete step by step solution:
The kinetic energy is given as,
$K.E = \dfrac{1}{2}m{v^2}$
From the above formula, we can say that kinetic energy is directly proportional to the velocity of the particle. Given that the kinetic energy of the particle is continuously increasing, therefore, we can say that the velocity also increases. Let us see each option and see whether the option is true or not.
Option A tells that the resultant force acting on the particle must be parallel to the velocity at all instants. This means that the resultant force and velocity will make an angle zero degree. This need not be a necessary condition. It is only a special case option B. Therefore option is not true
Option B tells us resultant force on the particle must be at an angle less than $90^\circ$ all the time. This is possible because only if the resultant force is less than the cosine value will be positive. SO it will have a positive component. Only if this is true the work done will be positive. Because we know that, $Work Done = Fd\cos \theta$. IF kinetic energy is increasing then the corresponding should also be a positive value. Therefore this option is true.
Option C does not give us detailed information about the direction of the velocity.
Option D is true as we have already seen from the formula, the velocity will keep on increasing if kinetic energy is increasing. This in turn makes the magnitude of linear momentum mv also increases continuously.
Therefore option B and option C both are true.

Note:
When an object is acted upon by several forces, then the resultant force is the force that alone produces the same acceleration provided by all other forces. The reason why the resultant force is useful is that it allows us to think about several forces as though they were a single force. To determine the effect that several forces have on an object, we only need to determine the effect that a single force has.