Question

CURRENT OBJECTIVE Interpret the relationship between the velocity function and acceleration function Question The position of a car traveling along a highway is given by the function $s(t) = -t^3 + \frac{9t^2}{2} + 12t - 5$ where $t \ge 0$ is measured in seconds and $s$ is measured in meters. On what interval(s) is the car speeding up? (Enter your answer in interval notation. If entering more than one interval write the intervals as a union.) Sorry, that's incorrect. Try again? (-1,4)

          CURRENT OBJECTIVE
Interpret the relationship between the velocity function and acceleration function
Question
The position of a car traveling along a highway is given by the function $s(t) = -t^3 + \frac{9t^2}{2} + 12t - 5$ where $t \ge 0$ is
measured in seconds and $s$ is measured in meters. On what interval(s) is the car speeding up?
(Enter your answer in interval notation. If entering more than one interval write the intervals as a union.)
Sorry, that's incorrect. Try again?
(-1,4)
        
Show more…
CURRENT OBJECTIVE
Interpret the relationship between the velocity function and acceleration function
Question
The position of a car traveling along a highway is given by the function s(t) = -t^3 + (9t^2)/(2) + 12t - 5 where t ≥ 0 is
measured in seconds and s is measured in meters. On what interval(s) is the car speeding up?
(Enter your answer in interval notation. If entering more than one interval write the intervals as a union.)
Sorry, that's incorrect. Try again?
(-1,4)

Added by Rebecca P.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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CURRENT OBJECTIVE Interpret the relationship between the velocity function and acceleration function Question Time t is measured in seconds and s is measured in meters. On what interval(s) is the car speeding up? (Enter your answer in interval notation. If entering more than one interval, write the intervals as a union.) Sorry, that's incorrect. Try again? (-1, 4)
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Transcript

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00:01 So in this problem, we are given the relation of the velocity of the car versus time.
00:09 So in part a, i want to describe what happened to the car at time t equal to zero.
00:14 So as we can see that at t equal zero, yeah, at t equal to zero, we see that the velocity begin decreasing, right? so at t equal to zero, so the car start decelerating.
00:32 Okay.
00:39 So cars start accelerating at t equal 1.
00:42 And part b, how does the car average velocity between 2 equal 0 to t equal 1 compared to the average velocity between t equal 1 and equal 5? so from t equal, so part b, from t equals 0 to t equal 1, we can easily see that the average velocity is over here, right? so it's 10 meters per second.
01:06 V bar is 10 meters per second from 0 to 1.
01:11 And from 1 to 5, so again, we see that it's right here, right? it's just the middle of the highest position, lowest position, which is over here.
01:21 So it's also 10.
01:23 V bar equal 10 meters per second.
01:26 So this is from 1 to 5.
01:27 So in that sense, the average velocity of these two intervals are the same.
01:34 And part c says that what is the displacement of the car from 0 to 0.
01:39 To 7.
01:43 So because we basically have three stages, the first stage is from 0 to 1, right? so the displacement from 0 to 1, let's say it's x01 equal half.
01:57 So t is from 0 to 1, right? so it's 1.
02:00 And times the, so basically we're just calculating the area of this triangle, all right? so times 20.
02:11 So this gives you 10 meters.
02:13 And then the second stage is from 1 to 5.
02:16 So we need to calculate the area of this triangle.
02:21 X15 equal half times so 5 minus 1 and times 20.
02:30 So this gives you 40 meters.
02:36 And then it's from 5 to 7.
02:41 We need to calculate this area.
02:46 So x 5 to 7 equal, because as you can see that the velocity is negative in this area, right? so the area here is also negative.
02:55 So it equals half, negative half, and the time is from 5 to 7, 7 minus 5, and times 20...
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