A race car moves such that its position fits the relationship x = (6.0 m/s) t +
ID: 1526765 • Letter: A
Question
A race car moves such that its position fits the relationship
x = (6.0 m/s)t + (0.85 m/s3)t3
where x is measured in meters and t in seconds.
(b) Determine the instantaneous velocity of the car at t = 3.3 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 = 0.20 s
t = 0.10 s
t = 0.40 s
________ m/s (Use the interval from t = 3.10 s to 3.50 s.)t = 0.20 s
_______ m/s (Use the interval from t = 3.20 s to 3.40 s.)t = 0.10 s
_______ m/s (Use the interval from t = 3.25 s to 3.35 s.)Explanation / Answer
b) Here's the answer using differential calculus:
Instantaneous velocity = dx/dt = 6.0 m/s + (3)(0.85)(t^2);
Evaluated at 3.3 seconds:
Instantaneous velocity =33.77 m/s