The function

Question

The function $s(t)$ represents the position of an object at time t moving along a line. Suppose $s(2)=136$ and $s(3)=156$ . Find the average velocity of the object over the interval of time $[2, 3]$ .

Accepted Answer

Welcome back. Everyone. In this problem, a particle moves along a line and its position at any time T in seconds is given by the function P of T, given that P of five equals 10 and P of eight equals 40. What is the average velocity of the particle over the time interval from T equals five to T equals eight A says it's 10 units per second. B 15 units per second, C 20 units per second and D 30 units per second. Now, if we're going to figure out the average velocity, let's ask ourselves, what do we know? Well, recall, OK, that the average velocity is going to be equal to the change in position. OK. So we'll need to know our start and final position divided by the change in time. So we'll also need to know our initial and final times. Now, in this case here, to figure out the average velocity, we want to find the change in position divided by the change in time from T equals five to T equals eight. And we know the positions at both of those times. So if we make a note of those, if we find those changes, then we should be able to solve for the average velocity. Now, what do we already know? Well, we know that PF five equals 10, what that statement tells us is that when our time equals five seconds, then our position equals 10. OK? Or 1010 units of whatever those units may be. So we can say then that when T equals five P equals 10. And from our other statement that P of eight equals 40 that tells us that when T equals eight seconds, OK, let me just write that properly here. Then P is equal to 40 units. Ok. So now what this tells us then is that our average velocity is going to be equal to our change in position from 40 units to sorry from 10 units to 40 units. That's 40 minus 10 units divided by our change in time, which is going to be eight seconds minus five seconds, 40 minus 10 equals 38 minus five equals three and 30 divided by three equals 10. So our average velocity is 10 units per second. When we look back at our answer choices that tells us a is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

The function ﻿s(t)s(t)s(t)﻿ represents the position of an object at time t moving along a line. Suppose ﻿s(2)=136s(2)=136s(2)=136﻿ and ﻿s(3)=156s(3)=156s(3)=156﻿ . Find the average velocity of the object over the interval of time ﻿[2,3][2, 3][2,3]﻿ .

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The function $s(t)$ represents the position of an object at time t moving along a line. Suppose $s(2)=136$ and $s(3)=156$ . Find the average velocity of the object over the interval of time $[2, 3]$ .