# The position of a body is s=25/(t+5) in the interval -4≤t≤0 with s in meters and t in seconds. Find: a. the body's displacement and average velocity for the given time interval b. the body's speed and acceleration at the endpoints of the interval c. when, if ever, during the interval does the body change direction

## Expert Answers The position of the body at time t is given by s = 25/(t + 5). The time interval under consideration is [-4, 0]

The displacement during this interval is (25/(0 + 5) - 25/(-4 + 5)) = 25(1/5 - 1) = -20 m. The average velocity is -20/(4) = -5 m/s

The instantaneous velocity of the body at any moment t is s' = -25/(t + 5)^2. At t = 0, the velocity is -25/25 = -1 m/s and at t = -4, the velocity is -25/1 = -25 m/s

The instantaneous acceleration of the body at any moment t is 50/(t + 5)^3. At t = 0, the acceleration 0.4 m/s^2. At t = -4, the acceleration is 50 m/s^2

The velocity of the body negative throughout the interval, therefore it does not change direction.

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