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 can use the formula for average speed:
Average speed = total distance / total time
In this case, we need to calculate the total distance traveled by the car between 0 seconds and 4 seconds, as well as the total time taken.
To calculate the distance, we need to find the displacement of the car between 0 seconds and 4 seconds. Displacement is the change in position.
Given that the position of the car at any time t is given by x = 10t - t^2, we can calculate the displacement by finding the difference in position at the two given times:
Displacement = x(4s) - x(0s)
Plugging in the values, we have:
Displacement = (10(4) - (4)^2) - (10(0) - (0)^2)
Simplifying further:
Displacement = 40 - 16 - 0 + 0
Displacement = 24
Now, we can calculate the average speed:
Average speed = Displacement / total time
Total time = 4s - 0s
Total time = 4s
Average speed = 24 / 4
Average speed = 6 m/s
Therefore, the average speed between 0 seconds and 4 seconds is 6 m/s.