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).

thanks

What’s the answer then I need some help here what’s the answer!!! Please

Anyone there please my assignment is due tomorrow

Answer

To answer this question, we need to determine the position of the race car at different points in time and calculate the instantaneous and average velocities. Let's break down each part of the question:

(a) Plotting the graph of the car's position versus time:
To plot the graph, we need to calculate the position of the car for various values of time. The equation given describes the position of the car as a function of time:

x = (5.0 m/s)t + (0.75 m/s^3)t^3

We can choose a range of values for t and calculate the corresponding x values. For example, let's choose t values from 0 to 5 seconds in increments of 0.5 seconds:

For t = 0, x = (5.0 m/s)(0) + (0.75 m/s^3)(0^3) = 0 meters
For t = 0.5, x = (5.0 m/s)(0.5) + (0.75 m/s^3)(0.5^3) = 0.625 meters
For t = 1.0, x = (5.0 m/s)(1.0) + (0.75 m/s^3)(1.0^3) = 5.75 meters

Continuing this process, we can calculate the position of the car for different values of t. Once we have these values, we can plot them on a graph with time (t) on the x-axis and position (x) on the y-axis. Connecting the points will give us a visual representation of the car's position versus time.

(b) Calculating the instantaneous velocity at t = 4.0 s:
To determine the instantaneous velocity, we need to find the derivative of the position equation with respect to time (dx/dt). Taking the derivative of the given equation:

dx/dt = (5.0 m/s) + 3(0.75 m/s^3)t^2

Now, we can substitute t = 4.0 s into this equation to find the instantaneous velocity at that specific time:

v_inst = (5.0 m/s) + 3(0.75 m/s^3)(4.0 s)^2
= (5.0 m/s) + 3(0.75 m/s^3)(16 s^2)
= (5.0 m/s) + 3(0.75 m/s^3)(256 s^2)
= (5.0 m/s) + (576 m/s)
= 581.0 m/s

Using time intervals of 0.40 s, 0.20 s, and 0.10 s, we can repeat the above process to find the instantaneous velocities at those times.

(c) Comparing the average velocity during the first 4.0 s with the results of (b):
To calculate the average velocity during the first 4.0 seconds, we can use the formula:

average velocity = total displacement / total time

The total displacement can be found by evaluating the position equation at t = 4.0 s using the formula given:

x = (5.0 m/s)t + (0.75 m/s^3)t^3
For t = 4.0 s, x = (5.0 m/s)(4.0 s) + (0.75 m/s^3)(4.0 s)^3

We can subtract the initial position (t = 0) from the final position (t = 4.0 s) to find the displacement. Then, divide the displacement by 4.0 s to calculate the average velocity during the first 4.0 seconds.

Once we have the average velocity, we can compare it with the results obtained for the instantaneous velocities at t = 4.0 s using different time intervals in part (b).

By following these steps, we can answer each part of the question and analyze the race car's motion.

i don't know... teachers even cant... lol

(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.