Question

A particle is moving in a circle with uniform speed. It has: (this question has multiple correct options):
A. constant kinetic energy
B. constant acceleration
C. Constant velocity
D. constant displacement

Answer 1

Hint: To find the constant, let us try to check every option. To begin with let us assume a particle on a circular path. A quantity is said to be constant, if all the related quantities are constant. Since we know the formula for kinetic energy and acceleration we can use them.

Formula used:
$KE=\dfrac{1}{2}mv^{2}$ and $a=\dfrac{v^{2}}{r}$

Complete step by step answer:
Assume a particle of mass $m$ and uniform speed $v$ travels in a circular path of radius $r$, then:
1. the kinetic energy:
Since we know that, the kinetic energy of the particle is given by $KE=\dfrac{1}{2}mv^{2}$. Assuming that the mass $m$ doesn’t vary, we get $m$ as a constant. Also, since the particle has uniform speed $v$, $v$ is also a constant, then we get that the kinetic energy is also a constant.
2. the acceleration:
Since we know that, the acceleration due to centripetal force is given by, $a=\dfrac{v^{2}}{r}$. Clearly as the velocity $v$ and the radius $r$ of the circle are constant, acceleration $a$ will also remain a constant.
3. the velocity:
We know that velocity is the rate of change of displacement, since there is no displacement here velocity is equal to $0$.
4. displacement:
As told previously, there is no displacement.
Thus clearly, the kinetic energy and the acceleration are constant here.
Hence the answer is option A. constant kinetic energy and B. constant acceleration.

Note:
Speed is the rate of change of distance, it is a scalar quantity while velocity is the rate of change of displacement, it is a vector quantity. As distance is a scalar quantity i.e. is always positive while displacement is vector quantity, it is either positive, negative or equal.