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

Question

t 0 0.3 1.0 1.6 2
v(t) 0 24.5 27.8 28.3 29.0

Answer 1

Did you make your sketch?
then
Area (or distance) = (1/2)(.3)(0 + 24.5) + (1/2)(.7)(24.5+27.8) + (1/2)(.6)(27.8+28.3) + (1/2)(.4)(28.3+29.0)
= ....

I will let you do the arithmetic.

Answer 2

A = 0.5(b1 + b2)h
h = dx so the change in x
A = 0.5(v(0) + v(0.3))(0.3 - 0) + 0.5(v(0.3) + v(1))(1 - 0.3) + 0.5(v(1) + v(1.6))(1.6 - 1)
+ 0.5(v(1.6) + v(2))(2 - 1.6)
A = 0.5(0 + 24.5)(0.3) + 0.5(24.5 + 27.8)(0.7) + 0.5(27.8 + 28.3)(0.6)
+ 0.5(28.3 + 29.0)(0.4)
A = 3.675 + 18.305 + 16.83 + 11.46
A = 50.27 feet
The car covered approximately 50.27 feet during those 2 minutes.