If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height in meters t seconds later is given by y = 10t - 1.86t^2

Question

a) Find the average velocity over the given time in intervals:

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

Do I just plug each in like this?

y= 10(1) - 1.86(2)^2
y= 2.56 m/s

OR do I use this: s(t)= 4.9t^2 like:

= [4.9(2)^2 - 4.9(1)^2]/1
= 14.7 m/s

I am not sure which way is correct or if either way is correct? Please help and explain too.

Answer 1

the purpose of the question is to notice that your answer will approach a certain fixed value as the interval gets shorter and shorter.

I will do the third one, you do the rest

[1,1.1]

y1 = 10(1) - 1.86(1)^2 = 8.14
y2 = 10(1.1) - 1.86(1.1)^2 = 8.7494

average velocity over given interval = (8.7494-8.14)/(1.1-1) = 6.094