A train travels in a straight westward direction along a track. The speed of the

Question

A train travels in a straight westward direction along a track. The speed of the train varies, but it is measured at regular time intervals of 1/10 hour. The measurements for the first half hour are

time 0 .1 .2 .3 .4 .5
speed 0 10 15 18 20 22

Estimate the total distance traveled by the train during the first half hour by assuming the speed is a linear function of t on the subintervals. The speed in the table is given in miles per hour. Give your answer in miles (you need not include the units - just give the number). Use all six speed measurements in your estimate.

Hint: plot speed against time for the given time values. How far do you think the train went during the first .1 hour?

Explanation / Answer

average the speed over the time interval. (0+10)/2=5 for .1 (10+15)/2=12.5 for .1 (15+18)/2=16.5 for .1 (18+20)/2=19 for .1 (20+22)/2=21 for .1 .5+1.25+1.65+1.9+2.1= 7.4 distance

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