Who Drives At A Constant Speed Everywhere?

Classical Mechanics Level 2

Given that a car is moving on a circular path with uniform speed, then which of the following must be true?

Image Credit: Fast and Furious: Tokyo Drift.
Its velocity remains constant, but its acceleration changes Its velocity changes, but its acceleration remains constant Both its velocity and acceleration changes Both its velocity and acceleration remains constant

Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

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1 solution

The velocity continuously changes. It oscillates between 0 and the diametre of the circle. Acceleration is the rate of change of velocity. So, it changes too.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Svatejas Shivakumar; No, the magnitude of the velocity remains constant, only the direction changes. Therefore your comment that the magnitude of the velocity oscillates at all is false. Nice try though! 😉

Matthew Heinlein - 5 years ago

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Ok, so we are addressing a car that is already moving, nowhere was it stated that it was anything but a perfectly circular track so how is it the velocity, (speed at which it travels) or the rate of acceleration change, assuming that the track is perfectly circular and the car is travelling fast enough to maintain that perfectly circuitous path? At least one of the variables must be constant given those perameters. I realize that velocity may not be immediately calculable on a small scale, due to the fact that direction is part of the equation, but let's pretend for one second that the center of this circle is the center of the earth and this circle is a straight road around the earth, which would very clearly allow for direction to be determined, hence velocity would be calculable and if traveling at a constant speed, there would be no change in acceleration. Additionally, this is assuming that the car is travelling parallel to the ground, a fact that wasn't stated either. P.s. not really meant as a response to Matt, just posted that way.

Mike Connor - 5 years ago

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You're confusing the terms speed and velocity . Speed is a scalar term, which refers only to magnitude, i.e., m/s or mph. Velocity is a vector term, which includes speed and direction . Since the track is circular, the direction is constantly changing, so you have a constantly changing (i.e., angular) velocity with a constant speed. If the angular velocity is changing, then the angular acceleration is also changing.

Brian Egedy - 5 years ago

This is a poorly worded problem

Jake Flom - 5 years ago

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What are your suggestions to improve the problem's wording?

Sandeep Bhardwaj - 5 years ago

You can state the reason as​ the direction keeps on changing at very instant in case of circular motion. And the velocity and acceleration are vector quantities depending on the direction. So these also keep on changing.

Sandeep Bhardwaj - 5 years ago

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Nice problem sir!

Rishabh Tiwari - 5 years ago

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Thank you, Rishabh. :)

Sandeep Bhardwaj - 5 years ago

Sit, I have a doubt. I have learnt that in circular motion and uniform speed, the velocity changes but acceleration is 0 0 . Is this wrong or I am interpreting this question wrong?

Ashish Menon - 5 years ago

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