A particle moves along a straight line with continuous velocity meters per second for…
MATHEMATICS · Multi-part · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change
Problem
A particle moves along a straight line with continuous velocity v(t)=3t2−4t+1 meters per second for 0≤t≤2 seconds.
(a) Write a Riemann sum that approximates the particle’s displacement on [0,2] using the midpoint of each subinterval for a partition into n equal subintervals.
(b) Determine the exact displacement of the particle on [0,2] by evaluating the limit of your sum from part (a). Justify your transition from the finite sum to its limiting value.
(c) Compute the midpoint approximation when n=4. Compare this numerical result to the exact displacement found in part (b) and discuss why the approximation differs from the exact value.