Speed, change in velocity, and average acceleration

In summary, an automobile traveling north begins to make a turn at t = 0 and follows one-quarter of the arc of a circle of radius 10.5 m until t = 1.42 s when it is traveling east. The car maintains a constant speed throughout the turn. To find the car's speed, the distance equal to one quarter of the way around the circle must first be calculated by finding 1/4 of the circumference. From there, the speed and change in velocity during the turn can be determined, as well as the average acceleration during the turn.
  • #1
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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  • #2
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.)
 

1. What is the difference between speed and velocity?

Speed refers to the rate at which an object covers distance, while velocity takes into account the direction of motion. In other words, velocity is a vector quantity that includes both speed and direction.

2. How is average acceleration calculated?

Average acceleration is calculated by dividing the change in velocity by the time it takes to change. This can be expressed as: average acceleration = (final velocity - initial velocity) / time.

3. What is the relationship between speed and acceleration?

Acceleration is the rate of change of velocity, so an object with a constant speed will have a zero acceleration. However, if an object changes its speed, then it will also have a non-zero acceleration. In general, the greater the acceleration, the faster the change in speed.

4. How does an object's mass affect its acceleration?

According to Newton's Second Law of Motion, the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. This means that a heavier object will have a lower acceleration compared to a lighter object when the same force is applied.

5. Can an object have a constant speed but changing acceleration?

Yes, an object can have a constant speed but changing acceleration. This can occur when the object is moving in a circular path, where its speed remains constant but its direction is constantly changing, resulting in a changing acceleration.

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