Car speeding up around a circle

[ooccoo]

Homework Statement

A car is being driven around in circles. The radius of the circle being made is R = 150.0 m. At t = 0, the car is on the left edge of the circle (therefore it is in the −x direction away from the center of
the circle if your origin is placed at the center), and it is moving in the +y direction. The initial speed is 12.0 m/s. However,
it is speeding up, with dv/dt = 1.00 m/s^2.

(a) What are the values of the displacement, velocity, and acceleration at t = 0?

(b) At time t = 10.83 s, it is now directly in the +y direction from the center of the
circle. What are the values of the displacement, velocity and acceleration?

(c) What was the average acceleration between t = 0 and t = 10.83 s?

(d) What is the value of t when you return to the position where you started?

Homework Equations

a=(dv/dt)(v-hat) - (v^2/R)(r-hat)

the hats are a function of where you are, and always point in different directions

and I believe a-hat would = a(vector) / |a (vector)| <<Absolute value... like magnitude.

The Attempt at a Solution

For a.) I believe that displacement would be 0 since the car hasn't moved. Velocity would be 12m/s in the +y direction, and acceleration would be 1.00 m/s^2 since acceleration is the derivative of velocity

For B, I start to get lost. I believe that I need to use the equation: [a=(dv/dt)(v-hat) - (v^2/R)(r-hat)]

I know that velocity is tangent to the circle and if the speed was constant, the acceleration would point directly at the center of the circle(making this problem easier) but instead it is point slightly forward

but I am getting thrown off by the fact that we're given the amount of time that has passed and the distance traveled (a fourth of the circumference)

any help would be greatly appreciated, my semester is almost over and I really want to understand this stuff before i go home for winter break. Thank you for your time!

 

[Doc Al]

For a.) I believe that displacement would be 0 since the car hasn't moved.

I suspect they mean displacement measured from the origin.

Velocity would be 12m/s in the +y direction, and acceleration would be 1.00 m/s^2 since acceleration is the derivative of velocity

Don't forget that it's moving in a circle. What about the radial component of acceleration?

For B, I start to get lost. I believe that I need to use the equation: [a=(dv/dt)(v-hat) - (v^2/R)(r-hat)]

You needed that for A as well.

I know that velocity is tangent to the circle and if the speed was constant, the acceleration would point directly at the center of the circle(making this problem easier) but instead it is point slightly forward

OK.

but I am getting thrown off by the fact that we're given the amount of time that has passed and the distance traveled (a fourth of the circumference)

It seems as if you are given too much information. Given the initial speed, radius, and tangential acceleration, you should be able to calculate the time to travel 1/4 of the circle. (Try it!)

Unfortunately the data do not seem consistent. Are you sure you are presenting the problem exactly as it was given?

 

[ooccoo]

In fact I am, which is why I'm confused. I'll try working with your reply and if i have an Aha! moment i will add on here. thank you!

 

[swsw]

Perhaps what they meant by acceleration is the centripetal acceleration? If the linear acceleration is given?

 

[haruspex]

I suspect they mean displacement measured from the origin.

I would think not. Displacement should mean change in position.

Don't forget that it's moving in a circle. What about the radial component of acceleration?

Perhaps what they meant by acceleration is the centripetal acceleration?

No, I agree with Doc Al they likely mean total acceleration, so the vector sum of the two. But it would have been better if they'd written the tangential acceleration as d|v|/dt.

Unfortunately the data do not seem consistent. Are you sure you are presenting the problem exactly as it was given?

It would match up if the radius were 120 m.

 

[Doc Al]

Displacement should mean change in position.

That's what it should mean, but from what point? (I suppose you can take the point where t=0, but that wasn't specified.)

It would match up if the radius were 120 m.

Good catch. I'll bet the 150 m is a typo.