Why are you accelerating yet remaining at a constant speed while going around a curve? [duplicate]

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.

marked as duplicate by Aaron Stevens, Thomas Fritsch, John Rennie homework-and-exercises StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Sep 23 at 4:31

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.

• It seems like the OP is specifically interested in why this acceleration does not cause a change in speed. – Aaron Stevens Sep 22 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 at 21:04
• Changing direction is not a sufficient condition for constant speed though – Aaron Stevens Sep 22 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 at 21:09
• @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 at 21:25