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.

Answer 1

Trapezoidal is involving averageing the heights
the 4 intervals are
[0,4] and [4,7.2] and [7.2,8.6] and [8.6,9]

the area of each trapezoid is (v(t1)+v(t2))/2 times width

for the first interval
the average between 0 and 0.4 is 0.2
the width is 4
4(0.2)=0.8

2nd
average between 0.4 and 1 is 0.7
width is 3.2
3.2 times 0.7=2.24

3rd
average betwen 1.0 and 1.5 is 1.25
width is 1.4
1.4 times 1.25=1.75

4th
average betwen 1.5 and 2 is 1.75
width is 0.4
0.4 times 1.74=0.7

add them all up
0.8+2.24+1.75+0.7=5.49

5.49
t=time
v(t)=speed
so the area under the curve is distance
covered 5.49 meters