Need Help with an Average Acceleration Problem

[xedothecat]

A car traveling with a constant speed of 14 m/s due west comes to an intersection where it makes a turn onto a southwest (45 degree) street. The car takes 5.2 seconds to complete the turn and the speed of the car does not change during this time. Find the average acceleration of the car. Report your answer in component form. Positive x points east and positive y points north.

 

[SammyS]

A car traveling with a constant speed of 14 m/s due west comes to an intersection where it makes a turn onto a southwest (45 degree) street. The car takes 5.2 seconds to complete the turn and the speed of the car does not change during this time. Find the average acceleration of the car. Report your answer in component form. Positive x points east and positive y points north.

Hello xedothecat. Welcome to PF !

According to the rules here at Physics Forums, you must show some effort before we can help you.

What have you tried?

Where are you stuck?

Since you're new here, I'll give a hint: Use the definition of average acceleration.

 

[xedothecat]

I drew a picture with the angle theta at 135 degrees. I tried to calculate the displacement vector's magnitude but I don't know the length of the other sides of the triangle I drew. I know that if the velocity is constant at 14 m/s and the turn takes 5.2 seconds, the total distance traveled is 72.8 meters and I know average acceleration is change in velocity over change in time. The change in time is 5.2 seconds and I don't know what the change in velocity is because if the velocity is constant, I don't get what I'm supposed to be calculating.

 

[frogjg2003]

Velocity is a vector. The car changed direction, so the velocity changed, even though the SPEED remained constant. Write down the components of the velocity before and after the turn. This gives you the change in velocity.

 

[Nickie]

The average acceleration of the car can be calculated using the formula a = (vf - vi)/t, where vf is the final velocity, vi is the initial velocity, and t is the time taken. In this case, the car's initial velocity is 14 m/s due west and the final velocity is still 14 m/s, as the speed does not change during the turn. Therefore, the average acceleration can be calculated as:

a = (14 m/s - 14 m/s)/5.2 s = 0 m/s^2

Since the car is turning onto a southwest street, the acceleration can be broken down into its x and y components. The x-component of acceleration can be calculated as ax = a*cos(45) = 0*cos(45) = 0 m/s^2. The y-component of acceleration can be calculated as ay = a*sin(45) = 0*sin(45) = 0 m/s^2.

Therefore, the average acceleration of the car is 0 m/s^2 in both the x and y directions. This means that the car is not accelerating in either direction and is maintaining a constant speed and direction during the turn.