Speedometer readings for a motorcycle at 12-seconds intervals are given in the table.

Question

Speedometer readings for a motorcycle at 12-seconds intervals are given in the table.

t (sec)  0 12 24 36 48 60

v (ft/sec) 22 24 26 20 22 29

(a) Estimate the distance, in feet, traveled by the motorcycle during the time interval from 0 to 60 seconds using the velocities at the beginning of the time intervals.



(b) Give another estimate using the velocities at the end of the time periods.

Answer 1

Each interval is 12 seconds wide. If we use the beginning velocity to estimate the distance in the first interval, we get

12 sec * 22 ft/sec = 264 ft

If we use the ending velocity in the first interval, we get

12 sec * 24 ft/sec = 288 ft

Adding all the left-hand velocities,

12*(22 + 24 + 26 + 20 + 22) = 12*114 = 1368

If we use the ending velocities, we get

12*(24 + 26 + 20 + 22 + 29) = 12*121 = 1452