If an arrow is shot upward on Mars with a speed of 52 m/s, its height in meters t seconds later is given by

Question

y = 52t − 1.86t2.
(Round your answers to two decimal places.)

What is 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]

Answer 1

the average speed is the total distance divided by the time. The total distance is the integral of the velocity. So, for

(i) the total distance traveled is
∫[1,2] (52t − 1.86t^2) dt = 73.66 meters
since the interval length is 1 second, that is the average speed.

do the others in like wise.

Answer 2

Oops. My bad. I thought the equation was velocity. Since it is distance, the average speed is just the distance covered, divided by the time (y(b)-y(a))/(b-a)

For (i), then we have
y(2) = 96.56
y(1) = 50.14
so, the average speed is (96.56-50.14)/(2-1) = 46.42 m/s