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).
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).
Answers
(a) First of all, we can't draw graphs for you. I will assume that you have done that on your own.
(b) Apparently you are taking a physics course that assumes you do not know calculus. With calculus, you could calculate that the instantaneous velocity is
V = dx/dt = 5.0 + 3*(0.75)*t^2
= 5.0 + 2.25 t^2,
which is 41.0 m/s at t=4 s.
To approximate the instantaneous velocity using a 0.4 s time interval, you would calculate x(t) at t = 4.2 and 3.8 s, and divide the difference by the elapsed time, 0.4 s. That would result in V = (76.57 - 60.15)/0.4 = 41.1 m/s. Try the similar calculation yourself for intervals of 3.9 to 4.1 s, and 3.95 to 4.05 s.
(c) As the time interval gets less, you should get closer to the actual instantaneous velcoity at t=4.0 s.
(b) Apparently you are taking a physics course that assumes you do not know calculus. With calculus, you could calculate that the instantaneous velocity is
V = dx/dt = 5.0 + 3*(0.75)*t^2
= 5.0 + 2.25 t^2,
which is 41.0 m/s at t=4 s.
To approximate the instantaneous velocity using a 0.4 s time interval, you would calculate x(t) at t = 4.2 and 3.8 s, and divide the difference by the elapsed time, 0.4 s. That would result in V = (76.57 - 60.15)/0.4 = 41.1 m/s. Try the similar calculation yourself for intervals of 3.9 to 4.1 s, and 3.95 to 4.05 s.
(c) As the time interval gets less, you should get closer to the actual instantaneous velcoity at t=4.0 s.
thanks
i don't know... teachers even cant... lol
What’s the answer then I need some help here what’s the answer!!! Please
Anyone there please my assignment is due tomorrow
Answer