Magnitudes and Directions In Uniform Circular Motion

[Rodriesk]

Homework Statement

A biker is 40.0m to the east of a flag in a park, heading south at 10m/s. 30.0 seconds later, the biker is 40.0m north of the flag and heading east at 10.0m/s. For the biker in this 30.0s interval, what are:
a) the magnitude and direction of the displacement?
b) the magnitude and direction of the velocity?
c) the magnitude and direction of the acceleration?

Homework Equations

a=v^2/r

The Attempt at a Solution

The image attached shows how I've set up the problem. For a), my first thought was to multiply time and velocity to solve for distance (magnitude). For the direction, I thought about the triangle P1 and P2 form, and solved for the angle that the line joining those two points forms with the x-axis. My attempt at solving for magnitude makes sense to me, but I'm not sure about the answer for the direction.

For b), I already have the velocity, which is 10m/s, and I believe that would be the magnitude, however I'm unsure about the direction. The direction changes every second, and so does the velocity, so I think there would be multiple answers for the direction depending on the time we're taking into account.

For c), I think it's the easiest part, since I have the velocity and radius, I can use a = v^2 / r to solve for the acceleration magnitude, and if I understand the concept of circular motion, the direction of the acceleration is always headed toward the center. I'm confident about this one.

Thank you in advance for your replies.

 

[haruspex]

multiply time and velocity to solve for distance (magnitude)

Distance travelled, ∫|v|.dt, is not the same as the magnitude of the displacement, |∫v.dt|.

For the direction, I thought about the triangle P1 and P2 form, and solved for the angle that the line joining those two points forms with the x-axis.

Yes.

the magnitude and direction of the velocity?

The velocity is not constant. We are not even told whether the magnitude of the velocity is constant. So I suggest the question is asking about the average velocity. How is that defined?

the magnitude and direction of the acceleration?

Again, acceleration is not constant, and might not be constant in magnitude, so I would interpret this as the average acceleration.