   Chapter 2, Problem 18P

Chapter
Section
Textbook Problem

A race car moves such that, its position fits the relationshipx = (5.0 m/s)t + (0.75 m/s3)t3where x is measured in meters and t in seconds. (a) Plot a graph of the car's position versus time. (b) Determine the instantaneous velocity of the car at t = 4.0 s, using time intervals of 0.40 s, 0.20 s, and 0.10 s. (c) Compare the average velocity during the first 4.0 s with the results of part (b).

(a)

To determine
The plot of the displacement of the car.

Explanation

The displacement is given as a function of time.

The displacement is given as a function of time. The displacement is,

x=(5.0m/s)t+(0.75m/s3)t3

• x is the displacement of the car.
• t is the time.

Substitute 1.00s for t to find x .

x=(5.0m/s)(1.00s)+(0.75m/s3)(1.00s)3=5.75m

Substitute 2.00s for t to find x .

x=(5.0m/s)(2.00s)+(0.75m/s3)(2.00s)3=16.0m

Substitute 3.00s for t to find x .

x=(5.0m/s)(3.00s)+(0.75m/s3)(3.00s)3=35.3m

Substitute 4

(b)

To determine
The instantaneous velocity of the car at 4.00s .

(c)

To determine
Comparison of average velocity of the car in 0 to 4.00s with the instantaneous velocity at 4.00s .

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