Question

A race car moves such that its position fits the relationship x=(5.0 m/s t+ (0.75m /s³) t³ Where x is measured in meters and t in seconds. Compare the average velocity during the first 4.0 s with the results of determine the instantaneous velocity of the car at t 5 4.0 s

Answer 1

To compare the average velocity during the first 4.0 seconds and determine the instantaneous velocity at t = 4.0 s of the race car.

Step-by-step explanation:

The equation given is x = (5.0 m/s)t + (0.75 m/s³)t³, where x is the position in meters and t is the time in seconds.

The average velocity during the first 4.0 seconds can be found by calculating the change in position during that time interval and dividing it by the time. So, we substitute t = 4.0 s into the equation to find x at t = 4.0 s, and then calculate the average velocity using the formula:

1. Average velocity = (change in position) / (change in time)

Similarly, the instantaneous velocity at t = 4.0 seconds can be found by taking the derivative of the position equation with respect to time. The formula for instantaneous velocity is:

1. Instantaneous velocity = dx/dt

Substituting t = 4.0 s into the derivative gives the instantaneous velocity at t = 4.0 s.

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