Finding the magnitude of acceleration in 2D motion

In summary, the car is traveling at a speed of 35.2 m/s and experiences an average acceleration of 1.7 m/s^2 while entering and exiting the cloverleaf. The magnitude of the average acceleration is not the same as the change in velocity, as it only takes into account the change in magnitude of velocity.
  • #1
Dano1337
1
0

Homework Statement


A car moving due south at 20.0 m/s enters a highway cloverleaf. The car will exit the cloverleaf to merge with westbound traffic traveling at 29.0 m/s.

The time between entering the cloverleaf and exiting to merge with westbound traffic is 20.7 s. What is the magnitude of the average acceleration of the car?

For the units, use a ^ to indicate an exponent.

Your answer should have one digit after the decimal place.

Homework Equations


magnitude eq = v = sqrt (x^2)+(y^2)
average a = change in velocity / change in time

The Attempt at a Solution


1. sqrt ((20^2)+ ((29^2)) = 35.2 m/s
2. 35.2 / 20.7 = 1.7 s
any help or advice on where I'm going wrong would be very much appreciated. [/B]
 
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  • #2
Check the units on your last line (2)?
 
  • #3
Dano1337 said:
average a = change in velocity / change in time
Correct.
Dano1337 said:
magnitude eq = v = sqrt (x^2)+(y^2)
It says nothing about change in speed.
Dano1337 said:
magnitude of the average acceleration
Magnitude of change of velocity is not the same as change of magnitude of velocity.
 

1. What is 2D motion?

2D motion refers to motion that occurs in two dimensions, typically represented on a two-dimensional coordinate system. It involves movement in both the x and y directions, and can include both linear and circular motion.

2. How is acceleration defined in 2D motion?

Acceleration in 2D motion is defined as the rate of change of velocity in both the x and y directions. It is a vector quantity and is typically represented by the symbol "a".

3. What is the formula for calculating acceleration in 2D motion?

The formula for calculating acceleration in 2D motion is a = Δv/Δt, where Δv is the change in velocity and Δt is the change in time. This formula can also be broken down into its x and y components, where ax = Δvx/Δt and ay = Δvy/Δt.

4. How do you determine the magnitude of acceleration in 2D motion?

The magnitude of acceleration in 2D motion can be determined using the Pythagorean theorem, where the magnitude of acceleration (a) is equal to the square root of (ax² + ay²). This represents the overall acceleration of an object in two dimensions.

5. What units are used to measure acceleration in 2D motion?

Acceleration in 2D motion is typically measured in units of meters per second squared (m/s²) or feet per second squared (ft/s²). These units represent the change in velocity (in meters or feet) over a given time (in seconds), squared.

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