Question

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

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.

Answers

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

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