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A race car moves such that its position fits the relationship x = (4.0 m/s) t +

ID: 1651338 • Letter: A

Question

A race car moves such that its position fits the relationship

x = (4.0 m/s)t + (0.65 m/s3)t3

where x is measured in meters and t in seconds.

(a) A plot of the car's position versus time is which of the following?


(b) Determine the instantaneous velocity of the car at

t = 4.2 s,

using time intervals of 0.40 s, 0.20 s, and 0.10 s. (In order to better see the limiting process keep at least three decimal places in your answer.)

t = 0.40 s

t = 4.00 s

t = 0.20 s

    

t = 4.10 s

t = 0.10 s

t = 4.15 s


(c) Compare the average velocity during the first 4.2 s with the results of part (b).

The average velocity of  m/s is  ---Select--- much less than about the same as much greater than the instantaneous velocity.

Explanation / Answer

(1)

graph fit is 4th option because at t=0,x=0 and it will be parabola

so graph 4 is correct

(2) x=4t+0.65t^3

v=dx/dt=4+1.95t^2

at t=4.2

v=38.4 m/s

(c)average velocity=x(4.2)/4.2=64.96/4.2=15.47m/s

so average velocity is much less than instantaneous velocity