Motion Problem: Race Car's Position & Instantaneous Velocity at t = 3.5 s

[Rymac]

This problem seems simple enough, I guess I just don't really understand what it's looking for in the (b) portion.

A race car moves such that its position fits the relationship where x is measured in meters and t in seconds.
x = (5.0 m/s)t + (0.80 m/s³)t³

(a) Plot a graph of the car's position versus time. (Do this on paper. Your instructor may ask you to turn in this work.)

(b) Determine the instantaneous velocity of the car at t = 3.5 s, using time intervals of 0.40 s, 0.20 s, and 0.10 s.

Δt = 0.40 s ____________m/s

Δt = 0.20 s ____________m/s

Δt = 0.10 s ____________m/s


(c) Compare the average velocity during the first 3.5 s with the results of (d).
The average velocity of _14.8_ m/s is (*d1*) much less than (d2) about the same as (d3) much greater than the instantaneous velocity.

 

[Integral]

You need to show that you have but some kind of thought into this problem.

what is your definition of Average and instanenous velocity?

 

[quicknote]

I would approach this problem by first understanding the given relationship between the race car's position and time. From the equation x = (5.0 m/s)t + (0.80 m/s³)t³, we can see that the car's position is dependent on both its velocity and acceleration. This means that the car is accelerating as it moves, which is important to keep in mind when calculating its instantaneous velocity.

To answer part (a), I would plot a graph of the car's position versus time, with position on the y-axis and time on the x-axis. This will give us a visual representation of how the car's position changes over time.

For part (b), we are asked to determine the instantaneous velocity of the car at t = 3.5 s. To do this, we can use the formula for average velocity, which is Δx/Δt. This means we need to calculate the change in position (Δx) and the change in time (Δt) over different time intervals. By using smaller time intervals (0.40 s, 0.20 s, and 0.10 s), we can get a more accurate approximation of the car's instantaneous velocity at t = 3.5 s.

To answer part (c), we can compare the average velocity during the first 3.5 s (calculated from the given equation) with the results from part (b). This will give us an idea of how the car's velocity changes over time. If the average velocity is much less than the instantaneous velocity, it means that the car is accelerating at a faster rate. If the average velocity is about the same as the instantaneous velocity, it means that the car is moving at a constant velocity. And if the average velocity is much greater than the instantaneous velocity, it means that the car is decelerating.

Overall, this problem is asking us to understand the relationship between a car's position, velocity, and time. By using mathematical formulas and calculations, we can get a better understanding of how these factors change over time and how they are related to each other.