Question

If an object is moving on a curved path, then
which of the following physical quantities may be
constant during the motion? (Symbols have usual
meanings)
​

Answer 1

Answer:

(1) only

Explanation:

Let's analyze each option.

(1) $\frac{d}{dt}|v|$

this quantity corresponds to the rate of change of the module of the velocity, so it is basically the magnitude of the acceleration. In a uniform circular motion, the magnitude of the (centripetal) acceleration is

$a=\frac{v^2}{r}$

where v is the speed and r the radius: since both v and r can be constant, then this means that this quantity can be constant as well.

(2) $v$ (vector)

This quantity is the velocity. Velocity is a vector: this means it has both a magnitude (the speed) and a direction. In a uniform circular motion, the speed can be constant; however, we know that the direction is for sure not constant, since the object is constantly changing path: therefore, this quantity cannot be constant.

(3) $a$ (vector)

This quantity is the acceleration. Acceleration is a vector: this means it has both a magnitude (given by $v^2/r$) and a direction. In a uniform circular motion, the direction of the (centripetal) acceleration is towards the centre of the circle, perpendicular to the velocity: however, since the object is constantly changing direction, this means that also the direction of the acceleration is constantly changing, therefore this quantity cannot be constant.