Question

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 a

Recall that the average speed between times

t₁

and

t₂

is calculated usingv_ave =

y(t₂) − y(t₁)

t₂ − t₁

.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
	=	[67(1 + h) − 1.86(1 + h)2] − 65.14 h
	=	63.28h− blank  h2 h
	=	blank − blank h,   h ≠ 0

Answer 1