Velocity and acceleration vectors problem

In summary, the question is asking for the direction of the car's average acceleration vector as it rounds a 90 degree curve from east to south with constant speed. The answer is not simply 90 degrees, as the direction of the acceleration changes as the car turns. It can be visualized as a force exerted by the road on the car wheels, perpendicular to the car's motion. The average direction of this force can be found by taking the direction halfway through the turn.
  • #1
estie
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Homework Statement



A car, initially going eastward, rounds a 90 degree curve and ends up heading southward. If the speedometer reading remains constant, what is the direction of the car's average acceleration vector? the angle is measured "CCW from east".


Homework Equations





The Attempt at a Solution


i honestly do not know what the question is asking. what does it mean by rounding a 90 degree curve?
 
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  • #2
The car can't turn sharply; you must imagine it turning on a circular path - a rounded corner. Circular motion. A centripetal force is necessary to hold the car in circular motion. This force causes the car to accelerate in the direction of the force.

The direction of the force an acceleration change as the car turns. If you just average the initial direction and the ending direction when it completes the quarter circle turn, you should have the direction you are looking for.
 
  • #3
wouldn't it just be 90 degrees then?
am i not following correctly?
 
  • #4
is it possible for you to explain with an image?
 
  • #5
Can't do an image just now. Picture the car initially going east, but just beginning to turn south. There must be a force on the car directed to the south. This force is actually exerted by the road on the car wheels. Of course the force can do no work on the car or we could have perpetual motion - so the force is perpendicular to the motion of the car.

As the car turns a little more and is headed southeast, the force perpendicular to that is southwest.

Finally as the car completes the turn and is going almost south, he force is to the west.

Draw those 3 vectors and mentally average the directions. Or just take the direction half way through the turn.
 

Related to Velocity and acceleration vectors problem

What is velocity?

Velocity is a measure of the rate at which an object changes its position. It is a vector quantity, meaning it has both magnitude (speed) and direction.

What is acceleration?

Acceleration is the rate at which an object's velocity changes over time. It is also a vector quantity, and is measured in units of distance per time squared (such as meters per second squared).

How are velocity and acceleration related?

Velocity and acceleration are related in that acceleration is the change in velocity over time. This means that a change in velocity (speed or direction) will result in an acceleration, and vice versa.

How can I calculate acceleration from velocity?

To calculate acceleration from velocity, you can use the formula a = (vf - vi) / t, where a is acceleration, vf is the final velocity, vi is the initial velocity, and t is the time interval. This formula assumes that the acceleration is constant over the given time interval.

What are some real-world examples of velocity and acceleration?

Some examples of velocity and acceleration in everyday life include a car accelerating from 0 to 60 miles per hour, a person riding a bike and gradually increasing their speed, or a ball being thrown and changing direction as it moves through the air. These concepts are also important in fields such as engineering, physics, and sports science.

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