The position of a particle along a straight-line path is defined by s = (t3 - 6t2 - 15t + 7) ft, where t is in seconds. when t = 8 s, determine the particle’s (a) instantaneous velocity and instantaneous acceleration, (b) average velocity and average speed

1) Instantaneous velocity at t= 8 equals 81m/s

2) Instantaneous acceleration at t= 8 equals

3) Average velocity between 0 to 8 seconds equals 1 m/s.

4) Average speed between 0 to 8 seconds equals 23.31 m/s.

Explanation:

Given position as a function of time as

Now by definition of velocity 'v' we have

Thus velocity at t = 8 seconds equals

Now by definition of acceleration 'a' we have

Thus acceleration at t = 8 seconds equals

Part 2)

The average of any function is mathematically defined as

Using the given function of velocity and using the limits from t = 0 to t = 8 secs we get

the average speed is calculated as

Hence the average speed is calculated as

energy can cross the boundaries of a closed system in the form of heat and mass

explanation: