a car brakes to a halt in 5 seconds. The position of the car versus time is given by:

x = 10t - t^2

a) What is the average speed between 0 s. and 4 s.?

Thank you

To find the average speed between 0 seconds and 4 seconds, we need to find the total distance traveled during that time interval, and then divide it by the time taken.

The position of the car versus time is given by the equation: x = 10t - t^2.

To find the distance traveled, we need to calculate the change in position between the initial time, t1 = 0 seconds, and the final time, t2 = 4 seconds.

The change in position is given by:

Δx = x2 - x1

Substituting the values of t1 and t2:

Δx = (10t2 - t2^2) - (10t1 - t1^2)
= (10(4) - (4)^2) - (10(0) - (0)^2)
= (40 - 16) - (0 - 0)
= 24

So, the total distance traveled during the time interval from 0 seconds to 4 seconds is 24 units.

To find the average speed, we divide this distance by the time taken:

Average speed = Δx / Δt

In this case, Δt = t2 - t1 = 4 seconds - 0 seconds = 4 seconds.

Therefore,

Average speed = 24 / 4
= 6 units per second.

Hence, the average speed of the car between 0 seconds and 4 seconds is 6 units per second.