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

(1) only

Step-by-step explanation:

Let's analyze each option.

(1)
`(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=(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.