How Many Revolutions Does a Car Make From Rest to a Specific Acceleration?

[feedmeister]

# of Revolutions made

I had the same question as someone else here, but they figured it out but nothing was said in the post. As such, I was asked to make a new thread..
So, pretty much, I have this question:

1. Homework Statement
A car starts from rest on a curve with a radius of 110 m and accelerates at 1.20 m/s^2. How many revolutions will the car have gone through when the magnitude of its total acceleration is 2.20 m/s^2?


2. Homework Equations

theta (final)=theta (initial)+omega*(delta)t+(a*(delta)t^2)/2*r

3. The Attempt at a Solution

i just have no idea how to figure out the time or the distance (or the angle) it takes the car to get from one acceleration to another...

 

[BlackWyvern]

Total acceleration = vector sum of tangential acceleration and centripetal acceleration.
Solve for centripetal acceleration.

Ac = v^2/r
Solve for v.

Use a kinematic equation with v, you should be done.

 

[ogb p]

As a scientist, it is important to always provide a clear and detailed explanation for any scientific question or problem. In this case, the question is asking for the number of revolutions a car will go through when experiencing a change in acceleration. To solve this problem, we can use the equation for rotational motion, which is provided in the post.

First, we need to determine the initial angular velocity (omega) of the car. Since the car starts from rest, the initial angular velocity is 0. Next, we can use the given acceleration (1.20 m/s^2) and radius (110 m) to calculate the final angular velocity (omega) using the equation: omega = sqrt(a/r).

Once we have the final angular velocity, we can use the equation provided in the post to calculate the final angle (theta). However, we need to find the initial angle, which is also 0 since the car starts from rest.

Now that we have both the initial and final angles, we can use the formula theta (final) = theta (initial) + omega * (delta)t + (a * (delta)t^2)/2*r to solve for the time (delta t). Once we have the time, we can use it to calculate the distance traveled using the formula d = (1/2)at^2.

Finally, we can use the formula for circumference (C = 2*pi*r) to determine the number of revolutions the car has gone through. We divide the total distance traveled by the circumference to get the number of revolutions.

In summary, to determine the number of revolutions a car will go through when experiencing a change in acceleration, we need to calculate the initial and final angular velocities, find the time and distance traveled, and use the circumference formula to determine the number of revolutions. It is important to carefully analyze the problem and use appropriate equations to find the solution.