The velocity of a car was read from its speedometer at 10-second intervals and recorded in the table. Use the midpoint rule to estimate the distance (in miles) traveled by the car.

Question

t(s)= 0 10 20 30 40 50 60 70 80 90 100

v(mi/h)= 0 30 47 50 56 62 67 53 55 48 41

Answer 1

Convert the time (10s) into hrs by dividing by 3600. That gives you a delta t of 0.002778 hrs.

Calculate the midpoints of the velocities:

15.0 m/hr

38.5 m/hr

48.5 m/hr

53.0 m/hr

59.0 m/hr

64.5 m/hr

60.0 m/hr

54.0 m/hr

51.5 m/hr

44.5 m/hr

Multiply each midpoint by the delta t to get:

0.04167 mi

0.10694 mi

0.13472 mi

0.14722 mi

0.16389 mi

0.17917 mi

0.16667 mi

0.15000 mi

0.14306 mi

0.12361 mi

Add them all up to get a total of 1.35694 mi