Question

If an arrow is shot upward on Mars with a speed of 67 m/s, its height...

If an arrow is shot upward on Mars with a speed of 67 m/s, its height in meters t seconds later is given by

y = 67t − 1.86t2.


Find the average speed over the given time intervals.

(i)     [1, 2]
(ii)     [1, 1.5]
(iii)     [1, 1.1]
(iv)     [1, 1.01]
(v)     [1, 1.001]

Step 1

Recall that the average speed between times

t1

and

t2

is calculated usingvave =

y(t2) − y(t1)
t2t1

.We are given that

y = 67t − 1.86t2.

Evaluating at

t = 1,

we have

y(1) = 67(1) − 1.86(1)2 = 65.14.

Thus, the average speed between times 1 and 1 + h is as follows.

vave =
y(1 + h) − y(1)
(1 + h) − 1

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