Question

A race car moves such that its position fits the relationship

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

where 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 (b).

Answer 1

I have already answered this question. See my answer posted earlier.

Answer 2

b) Here's the answer using differential calculus:

Instantaneous velocity = dx/dt = 5.0 m/s + (3)(0.75)(t^2);

Evaluated at 4.0 seconds:

Instantaneous velocity = 5.0 + (2.25)(16) = 41 m/s