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We have to write a rap in physics, and it has to answer a prompt he gave us on this packet. The prompt for the verse I am writing is:

Pretend you are driving a car on the freeway going 65 mph. The freeway turns to the right and during the turn you are still going 65 mph. Explain why you are accelerating and yet going the same speed.

Can you help me answer it? I should be able to write lyrics after that.

BioPhysicist
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Potato Grill
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Explain why you are accelerating and yet going the same speed.

Acceleration occurs if there is a change in speed, or if there is a change in direction. While your car's speed doesn't change, its direction does. So it experiences an acceleration.

It all has to do with Newton's first law. The law basically says a body moving in a straight line at constant speed will continue to move in the same direction and at the same speed unless acted upon by an external force. This is due to the inertia of the body.

In order for your car to change direction it must be subjected to an external force. That force is the static friction force between your tires and the road, which is called the centripetal force, that allows you to change direction by continually pulling the car towards the center of the circular path of the car. The centripetal force opposes the centrifugal force (apparent force) that wants to keep the car moving in its original direction and speed, and that is really the inertia of the car. The centripetal force causes a centripetal acceleration towards the center the magnitude of which is

$$a_{\text{centripetal}}=\frac{v^2}{r}$$

Where $v$, in your case, is 65 mph, and $r$ is the radius of the circular path, which depends on how sharp a turn the car makes. The sharper the turn the greater the centripetal force and centripetal acceleration.

Hope this helps.

Bob D
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  • It seems like the OP is specifically interested in why this acceleration does not cause a change in speed. – BioPhysicist Sep 22 '19 at 21:03
  • @AaronStevens I thought I answered that by saying it is because it is changing direction. Perhaps I need to emphasize that point better. I will revise. – Bob D Sep 22 '19 at 21:04
  • Changing direction is not a sufficient condition for constant speed though – BioPhysicist Sep 22 '19 at 21:05
  • @AaronStevens Not sure what you are getting at. Are you saying that changing direction at constant speed is not acceleration? – Bob D Sep 22 '19 at 21:09
  • No, I am saying that the reason the speed doesn't change isn't because the direction is changing. You can have direction changes with speed changing as well. – BioPhysicist Sep 22 '19 at 21:10
  • @AaronStevens Of course. That's why I said you have acceleration if you have a change in speed or a change in direction, and my "or" is an inclusive "or" (and/or) – Bob D Sep 22 '19 at 21:11
  • You are explaining why there is an acceleration, but you are not explaining why in this scenario the speed is not changing. I think this is what the OP might be going for. Your answer doesn't explain why the speed is constant. It just explains why there is still an acceleration here. Although I agree the question isn't as clear as it could be on this point. – BioPhysicist Sep 22 '19 at 21:13
  • @AaronStevens Once again I feel like we are going around in circles. If I say acceleration is due to either a change in speed or a change in direction, or both, doesn't that mean I am saying the speed can be constant and there still be acceleration? I thought so. But maybe you can do a better job, so please post an answer. Regards, Bob – Bob D Sep 22 '19 at 21:18
  • I feel like this concept has been answered a lot on this site, so I am not going to answer. Your answer says the speed can be constant, yes. But your answer does not say why it actually is constant in this specific scenario. I think it is a fine answer though. Hopefully the OP can clarify, or mark your answer as accepted. Sorry that I could not be more clear :) – BioPhysicist Sep 22 '19 at 21:23
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    @AaronStevens Sorry if I seemed a little testy. Had a rough day. But as always I really do appreciate your input and guidance, particularly re Newtonian mechanics as that is not necessarily my strongest suit. Regards. – Bob D Sep 22 '19 at 21:25