The position of an object moving vertically along a line is gi...

Question

The position of an object moving vertically along a line is given by the function $s\left(t\right)=-16t^2+128t$ . Find the average velocity of the object over the following intervals.

$\left\lbrack1,4\right\rbrack$

Accepted Answer

Hi, everyone. Let's take a look at this practice problem dealing with average velocities. This problem says a projectile is launched upwards with its height given by the function H of T is equal to minus five T squared plus 60 T plus 10, where H is in meters and T is in seconds. Calculate the average velocity of the projectile over the interval of 1 to 6. We're given four possible choices as our answers. For choice A we have 10 m per second. Choice B we have 25 m per second. For choice C we have 15 m per second and for choice D we have 20 m per second. Now the question asks us to calculate the average velocity of the projectile over the interval of 1 to 6. So recall your definition for the average velocity that is gonna be the average, gonna be equal to our change in positions. In this case, our change in height will have H of six minus H of one divided by our change in time, which in this case is just gonna be six minus one. So what we need to do is calculate our heights at time. When T is equal to six and when T is equal to one. So we'll start off by using the equation that we were given in the problem to calculate those times. So four of six, that's gonna be equal to minus five, multiplied by six squared plus six, multiplied by six plus 10. So that means that age of six, it's gonna be equal to 190. We'll do the same thing for our height. We at one second, we'll have each of one is equal to minus five, multiplied by one squared plus 60 multiplied by one plus 10. That means that H one gonna be equal to 65. So we can take those two values and substitute them in to our expression for the average velocity. So we have, the average is equal to, for H six, that is 190. We'll have minus for H one, we have 65 and that whole quantity is gonna be divided by the quantity of six minus one. So when we plug those values to dark calculator, we'll have the average is equal to 25. And the units for this are gonna be meters per second since our HS were given in units of meters and RT was given in units of seconds. So they'll give me units of meters per second. So let's have meters in the numerator and seconds in the denominator. So this is the answer that we're actually looking for. And when I compare that to my answer choices, the correct answer choice turns out to be answer choice. B so I hope that this explanation has been useful and I'll see you in the next video.

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The position of an object moving vertically along a line is given by the function $s\left(t\right)=-16t^2+128t$ . Find the average velocity of the object over the following intervals.
$\left\lbrack1,4\right\rbrack$