Derivatives as rates of change The figure shows the velocity v or position s of

Question

Derivatives as rates of change

The figure shows the velocity v or position s of a body moving along a coordinate line as a function of time t. Use the figure to answer the questions. When is the body's acceleration equal to zero? The position of a body moving on a coordinate line is given by s = t2 - 4t + 10, with s in meters and t in seconds. When, if ever, during the interval 0 le t le 4 does the body change direction? At time t, the position of a body moving along the s-axis is s = t3 - 12t2 + 36t m. Find the total distance traveled by the body from t = 0 to t = 3.

Explanation / Answer

5) during the interval 0<=t <= 4 , body will change the direction .

because , ds/dt = 2t-4 . then at t=0 , ds/dt = -4 (means negative ). But at t=4 , ds/dt = +4 (means posivtive).

therefore body changes direction during the interval 0<=t <= 4.

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