# Circular motion

tubworld
A car initially traveling eastward turns north by traveling in a circular path at uniform speed. The length of the arc ABC is s metres, and the car completes the turn in t seconds.

What is the acceleration when the car is at B located at an angle of r degrees? Express your answer in terms of the unit vectors x and y component?

Determine its average acceleration during the t seconds interval.

Any hints to do this? What is the difference in ans between the 2? is there a need for calculus?

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Theoretician

For the first part, draw a diagram of what you think is happening and come up with a formula for the velocity (velocity not speed) of the car at any time in terms of the parameters you have. This is your starting point.

For the second part, a general hint is that any average is just the difference between the final situation and the initial situation divided by time (resolve).

I hope that I haven't given too much of a help but enough of a help to guide you to the method of finding solution. It was a fun problem I thought.

tubworld
but for the second pt, the final acceleration is = to the initial acceleration since the linear speed is constant and the only acceleration is the cetripetal acceleration.As such, it's tentamount to saying that the average acceleration is 0.

Homework Helper
acceleration has both a direction and a magnitude, so is a vector.

You have to find the vector average of the acceleration.

Defn: (average) accln is the (vector) change in velocity over time.

tubworld
Serioulsy, I am still confused. The velocity of the car is changing at all instances but its speed is kept constant. As such, I understand that there is acceleration but its due to a change in direction and not magnitude. So how do I express this?

Mentor
You need to review the basic facts of circular motion. When something travels in a circle at uniform speed, its acceleration is towards the center. Accordingly, this is called centripetal acceleration. (Look it up!)

Theoretician
tubworld said:
Serioulsy, I am still confused. The velocity of the car is changing at all instances but its speed is kept constant. As such, I understand that there is acceleration but its due to a change in direction and not magnitude. So how do I express this?

Consider the x and y directions of (constant) acceleration* separately and then combine them.

* The acceleration being the one that will transform your initial velocity to your final velocity in the given time.