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