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How To Find Distance Traveled Calculus. Find the total distance traveled by a body and the body's displacement for a body whose velocity is v (t) = 6sin 3t on the time interval 0 t /2. Then find the distance traveled in each direction, make all the distances positive and add them up.

Question Video Calculating the Total Distance Traveled
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The distance traveled in each interval is thus 4 times 20, or 80 feet, for a total of 80 + 80 = 160 feet. Then find the distance traveled in each direction, make all the distances positive and add them up. So the cat's position at t = 8 is s (8) = 12 feet.

Question Video Calculating the Total Distance Traveled

This section explores how derivatives and integrals are used to study the motion described by such a function. The applet shows a graph (in magenta) of the velocity for the car, in feet/second. This section explores how derivatives and integrals are used to study the motion described by such a function. We want to know the cat's change in position from t = 0 to t = 8, so we integrate the velocity function by looking at the areas on the graph.