# Finding the Velocity and Acceleration of a Car in Circular Motion

mrcheeses

## Homework Statement

A car enters the circular road with radius r = 200m at a
speed of v = 80km/h. A radar gun at O needs to rotate with constant angular
a) Determine the acceleration of the car at the instant right after it enters the circular
b) Determine the velocity and acceleration of the car at the instant when the radar
gun has rotated

## Homework Equations

v_r = dr/dt
v_θ = r(dθ/dt)
a_r = dr/dt - r(dθ/dt)^2
a_θ = r(d^2θ/dt^2) + 2(dr/dt)θ

## The Attempt at a Solution

I think I got a right.

I took derivatives of the radius which is zero, and integrated the angular acceleration. I then just plugged the numbers into the acceleration formulas and got a_r=0 (assuming t=0) and a_θ = 5 = a.

I am a bit unsure about the 2nd one because i am having trouble getting the equation of velocity and acceleration in terms of theta. I always end up with either the angular velocity, or time variable in there. Help appreciated.

Homework Helper

## Homework Statement

A car enters the circular road with radius r = 200m at a
speed of v = 80km/h. A radar gun at O needs to rotate with constant angular
a) Determine the acceleration of the car at the instant right after it enters the circular
b) Determine the velocity and acceleration of the car at the instant when the radar
gun has rotated

## Homework Equations

v_r = dr/dt
v_θ = r(dθ/dt)
a_r = dr/dt - r(dθ/dt)^2
a_θ = r(d^2θ/dt^2) + 2(dr/dt)θ

## The Attempt at a Solution

I think I got a right.

I took derivatives of the radius which is zero, and integrated the angular acceleration. I then just plugged the numbers into the acceleration formulas and got a_r=0 (assuming t=0) and a_θ = 5 = a.

I am a bit unsure about the 2nd one because i am having trouble getting the equation of velocity and acceleration in terms of theta. I always end up with either the angular velocity, or time variable in there. Help appreciated.
I am not sure what the question is in part b). Is it the speed of the car when it has rotated 2π radians?

r is constant, since it is a circle. So you don't need to worry about dr/dt

You first have to find how long it takes the car to make the full circle: Δt. Then find the Δv in that time.

AM