Postsecondary • 9mo.

A car is constantly speeding up clockwise on a circular track with a radius of 100 m. At a given moment, when the car is moving south, its total acceleration is 4.10m/s2 and makes an angle of exactly 3◦ with the radius. Suppose that the tangential acceleration is constant, how long will it take for the car to come back to exactly the same place?

Explanation from Alloprof

This Explanation was submitted by a member of the Alloprof team.

Hi

AlphaAquamarine7466,Thanks for coming to Alloprof :)

To solve this problem, we can use concepts from circular kinematics. First, we need to find the tangential component of acceleration, which is the acceleration that contributes to the car's velocity. This component can be found using the formula:

a_tangential = a_total * cos(θ)

where a_tangential is the tangential acceleration, a_total is the total acceleration (4.10 m/s² in this case), and θ is the angle between the total acceleration and the radius (3 degrees in this case, converted to radians.

Now, we can use the kinematic formula to find the time required to return to the same location:

Δθ = ω_initial * t + 0.5 * α * t^2

where Δθ is the total angle traveled (360 degrees or 2π radians to return to the same place), ω_initial is the initial angular velocity (0 because the car starts from rest), α is the angular acceleration, and t is the time we are looking for.

You should be able to solve your problem with this information :)

Sandrine