Question

If an arrow is shot upward on Mars with a speed of 68 m/s, its height in meters t seconds later is given by

y = 68t − 1.86t2.

(Round your answers to two decimal places.)

(a) Find the average speed over the given time intervals.

(b) Estimate the speed when t = 1.

Answer 1

(a) dy/dt = 68 - 3.72t

(b) 64.28m/s

Explanation:

Given y = 68t - 1.86t²

Average Speed is rate of chance of distance with respect to time. Written as dy/dt

To obtain dy/dt, we differentiate y with respect to t, doing that, we have

dy/dt = 68 - 2(1.86)t

= 68 - 3.72t

(a) dy/dt = 68 - 3.72t

(b) To estimate the speed when t = 1, we substitute t = 1 in dy/dt .

dy/dt at t = 1 is

68 - 3.72(1)

= 68 - 3.72

= 64.28

The speed at t = 1 is 64.28m/s