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Acceleration, Displacement, and Velocity

1. A car rounds a 1.20 km radius circular track at 89 km/h
Find the magnitude of the car's average acceleration after it has completed one-fourth of the circle.
Express your answer to two significant figures and include the appropriate units.

2. You walk 1260 m east and then 860 m south in a total time of 25 min .
A. Compute your displacement.
Enter the east and south components of the displacement separated by a comma.
B. Compute your average velocity in m/s.
Enter the east and south components of the velocity separated by a comma.

3. A circular racetrack with 250 m radius lies in the x-y plane and is centered at the origin. A car rounds the track counterclockwise starting at the point (250 m , 0).
A. Find the total distance traveled after one-quarter lap.
Express your answer with the appropriate units.
B. Find the total displacement after one-quarter lap.
Enter the x and y components of the displacement separated by a comma.
C. Find the total distance traveled after one-half lap.
Express your answer with the appropriate units.
D. Find the total displacement after one-half lap.
Enter the x and y components of the displacement separated by a comma.
E. Find the total distance traveled after one complete lap.
Express your answer with the appropriate units.
F. Find the total displacement after one complete lap.
Enter the x and y components of the displacement separated by a comma.

Solution Preview

Please refer to the attachment.

1. A car rounds a 1.20 radius circular track at 89
Find the magnitude of the car's average acceleration after it has completed one-fourth of the circle.
Express your answer to two significant figures and include the appropriate units.

Solution:
y
Vf Car's position at t = t

R=1.2 km Vi

Car's position at t=0
x

Initial and final velocity (after one fourth circle) of the car are shown in the fig.. Change in velocity = Final velocity - Initial velocity. To determine the change in velocity we draw the velocity vector diagram.

Vi
(Vf - Vi)

Vf

In the above vector diagram Vf - Vi = ΔV represents the change in the velocity in time t (time taken to complete one fourth circle).

Magnitude of the change in velocity ΔV = √(Vi2+Vf2) = √(892+892) = 125.87 km/hr

Actual distance travelled by the car = ¼ ...

Solution Summary

Acceleration, displacement and velocity is examined. The expert computes the average velocity and displacement.

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