Calculus Please Help

Question

A radar gun was used to record the speed of a swimmer (in meters per second) during selected times in the first 2 seconds of a race. Use a trapezoidal sum with 4 intervals to estimate the distance the swimmer covered during those 2 seconds. Give a 2 decimal place answer and include units.

t     0   0.4  1.0    1.5     2

v(t) 0    4    7.2    8.6   9.0

Answer 1

Hi Kyle,

 

Distance is simply the speed times the time (d = vt), however, in this case the speed varies with time which makes it a little more difficult. In either case the answer is the value of the area under the curve. (note that the x axis is time and the y axis is speed). So plot the points on a piece of paper and connect the points with lines. This should result in 4 trapezoids. Find the area of these trapezoids and add them up. This is your answer.

 

John