Calculating Car's Acceleration in 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?

 

[Theoretician]

I've completed your problem.

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.

 

[Fermat]

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?

 

[Doc Al]

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]

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.