A race car moves such that its position fits the relationship x = (4.0 m/s)t + (
ID: 1883503 • Letter: A
Question
A race car moves such that its position fits the relationship
x = (4.0 m/s)t + (0.80 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 = 4.5 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 = 4.30 s
t = 0.20 s
t = 4.40 s
t = 0.10 s
t = 4.45 s
(c) Compare the average velocity during the first 4.5 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.
x (m) 220 00- 180 160 140 120- 100 80 40 20 t (s) 1.00 2.00 3.00 4.00 5.00 6.00
Explanation / Answer
C) we know that how a average velocity of m/s is much lesser than about the same as much greater than the instantaneous velocity average speed of a particle in a given time is never less than magnitude of average velocity.
Then we see that, it is possible to have a situation where
|dv/dt| is not equal to zero but d|v|/dt =0
the average velocity of a particle is zero in a time interval. it is possible that the instantaneous velocity is never zero in that interval.
D)the average velocity of a particle moving along a straight line is zero in a time interval. it is possible that the instantaneous velocity is never zero in that interval. We will exaplain in detail that :The average velocity is displacement /time but average speed is distance/ time. Since distance is always greater than or equal to displacement, it is evident that average speed is either equal to or greater than average velocity