Question

A body moves on a coordinate line such that it has a position s = f(t) = t² - 6t + 5 on the interval 0 ≤ t ≤ 8, with s in meters and t in seconds. Find the body's displacement a.

Answer 1

To determine the body's displacement on a coordinate line, evaluate the position function at the beginning and end of the time interval, then subtract the initial position from the final position. In this case, the displacement over the time interval from 0 to 8 seconds is 16 meters.

Step-by-step explanation:

The student’s problem involves finding the displacement of a body moving along a coordinate line. The body's position function is given by s = f(t) = t² - 6t + 5, and we need to calculate the displacement over the interval from t = 0 to t = 8 seconds. Displacement is the body's overall change in position, which can be found by evaluating the position function at the endpoints of the interval and subtracting the initial position from the final position.

To find the displacement a, you plug in the time values into the position function:

• 
  
• s(0) = (0)² - 6(0) + 5 = 5 m
• 
  
• s(8) = (8)² - 6(8) + 5 = 64 - 48 + 5 = 21 m

So the displacement a is:

a = s(8) - s(0) = 21 m - 5 m = 16 m