MATHEMATICS · Multi-part · AP · Calculus BC · Applications of Integration · Applications of Integration
Problem
A particle travels along the curve given by y=f(x)=x2 for 0≤x≤3. The x–coordinate is measured in meters.
(a) Compute f′(x) and write, but do not evaluate, a definite integral that represents the distance traveled by the particle from x=0 to x=3. Include appropriate limits of integration and units.
(b) Evaluate the integral exactly to determine the distance traveled, in meters.
(c) The particle moves from (0,0) to (3,9) in 6 seconds. Using your result from part (b), calculate its average speed over the 6–second interval. State units as part of your answer.