Speed, change in velocity, and average acceleration

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SUMMARY

The discussion focuses on calculating the speed, change in velocity, and average acceleration of an automobile making a quarter turn along a circular path with a radius of 10.5 meters over a time span of 1.42 seconds. The correct approach involves first determining the circumference of the circle using the formula \(C = 2\pi r\), then calculating one-quarter of that distance to find the distance traveled. The speed can be calculated by dividing this distance by the time, while the change in velocity and average acceleration can be derived from the initial and final velocities during the turn.

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  • Understanding of circular motion and its properties
  • Familiarity with the formula for the circumference of a circle
  • Basic knowledge of speed, velocity, and acceleration concepts
  • Ability to perform calculations involving time and distance
NEXT STEPS
  • Calculate the circumference of a circle using the formula \(C = 2\pi r\)
  • Learn how to derive speed from distance and time
  • Understand the difference between speed and velocity in physics
  • Explore the concept of average acceleration in circular motion
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Students studying physics, particularly those focusing on kinematics and circular motion, as well as educators looking for examples of real-world applications of these concepts.

Debbie-Marie
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Homework Statement


At t = 0, an automobile traveling north begins to make a turn. It follows one-quarter of the arc of a circle of radius 10.5 m until, at t = 1.42 s, it is traveling east. The car does not alter its speed during the turn.
Find the car's speed.
Find the change in it's velocity during the turn
Find it's average acceleration during the turn

Homework Equations


Speed- m/s
Change of velocity

The Attempt at a Solution


When I first read this problem, the first thing I did was draw a circle. With the circle, I made a 1/4th arc and separated into segments with 10.5 m. Then I outlined the whole arc's time would be 1.42 seconds. So I added the 4 segments and divided them by 1.42 to get the speed. Didn't work. The other questions fall into getting this one. Help would be appreciated!
 
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Hello Debbie-Marie,

Welcome to Physics Forums!
Debbie-Marie said:
When I first read this problem, the first thing I did was draw a circle. With the circle, I made a 1/4th arc and separated into segments with 10.5 m. Then I outlined the whole arc's time would be 1.42 seconds. So I added the 4 segments and divided them by 1.42 to get the speed. Didn't work. The other questions fall into getting this one. Help would be appreciated!
I'm not quite sure I follow you methods. The problem might be in adding the 4 segments together before dividing by the time. But I'm not quite sure what you meant though.

Let's start over. You already know the time it takes to travel one quarter of the way around the circle. So the first order of business is to find the distance equal to one quarter of the way around the circle. Perhaps, ask yourself these questions.

If you know the radius of a circle, what is the entire circumference of the circle?

So, if you know the radius of a circle, what is 1/4 the distance around that circle?

From there, you should be able to calculate the speed and such. :wink:

(also, you should show us your calculations in the future.)
 

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