Acceleration in Two Dimensions

In summary, the problem involves a car traveling due north around a semicircle with a radius of 500 m at a constant speed of 20 m/s. The questions are: A) How long does this take? B) What is the magnitude and direction of the average acceleration? The relevant equation for the problem is a = Δvx/Δt(xhat)+Δvy/Δt(yhat), and the attempt at a solution involves drawing a diagram of the half circle and determining the Δt for part A.
  • #1
Violagirl
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Homework Statement



A car initially traveling due north goes around a semicircle having a radius of 500 m at a constant speed of 20 m/s. A) How long does this take? B) What is the magnitiude and direction of the average acceleration?

Homework Equations



a = Δvx/Δt(xhat)+Δvy/Δt(yhat)


The Attempt at a Solution



I'm stumped as to how to start this problem. I drew out a half circle with the radius showing 500 m for the distance. I'm not sure if I'm missing a formula or what as I didn't see anything relevant for circles on my formula sheet from my class. Any help is appreciated.
 
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  • #2
Violagirl said:

Homework Statement



A car initially traveling due north goes around a semicircle having a radius of 500 m at a constant speed of 20 m/s. A) How long does this take? B) What is the magnitiude and direction of the average acceleration?

Homework Equations



a = Δvx/Δt(xhat)+Δvy/Δt(yhat)


The Attempt at a Solution



I'm stumped as to how to start this problem. I drew out a half circle with the radius showing 500 m for the distance. I'm not sure if I'm missing a formula or what as I didn't see anything relevant for circles on my formula sheet from my class. Any help is appreciated.

For one thing for motion in two dimensions, acceleration is a vector quantity. It has x and y components. You don't add them. But you didn't do part A yet. What's the Δt?
 

What is acceleration in two dimensions?

Acceleration in two dimensions refers to the rate of change of velocity in both the horizontal and vertical directions. It is a vector quantity, meaning it has both magnitude and direction.

What is the formula for calculating acceleration in two dimensions?

The formula for acceleration in two dimensions is a = (vf - vi) / t, where vf is the final velocity, vi is the initial velocity, and t is the time interval.

How does acceleration in two dimensions differ from acceleration in one dimension?

Acceleration in one dimension only considers changes in velocity along one axis, while acceleration in two dimensions takes into account changes in velocity along both the horizontal and vertical axes.

What are some real-life examples of acceleration in two dimensions?

Some real-life examples of acceleration in two dimensions include the motion of a projectile, such as a baseball being thrown or a rocket being launched, and the motion of an object in circular motion, such as a car going around a curved track.

How can acceleration in two dimensions be graphically represented?

Acceleration in two dimensions can be graphically represented using a vector diagram, where the magnitude and direction of the acceleration are shown using arrows. It can also be represented on a position-time or velocity-time graph as a curve with changing slope.

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