Question

The velocity of a box traveling along the axis is shown as a function of time in the figure below. If the box is at x = 0 when t = 0, answer the following. v_x (m/s) 20 10 0 -10 5 10 15 t (s) (a) What is the object's acceleration (in m/s^2) between 0 and 3.00 s? (Indicate the direction with the sign of your answer.) m/s^2 (b) What is the object's acceleration (in m/s^2) between 3.00 s and 8.00 s? (Indicate the direction with the sign of your answer.) m/s^2 (c) What is the object's acceleration (in m/s^2) between 13.0 s and 18.0 s? (Indicate the direction with the sign of your answer.) m/s^2 (d) At what time(s) (in s) is the object moving with the lowest speed? (If there is more than one time, enter the times from smallest to largest. If there is only one time, enter 0 in the second box.) s (smaller value) s (larger value) (e) At what time (in s) is the object farthest from x = 0? s (f) What is the final position x (in m) of the object at t = 18 s? m (g) Through what total distance (in m) has the object moved between t = 0 and t = 18 s? m

          The velocity of a box traveling along the axis is shown as a function of time in the figure below. If the box is at x = 0 when t = 0, answer the following.

v_x (m/s)
20
10
0
-10
5 10 15 t (s)

(a) What is the object's acceleration (in m/s^2) between 0 and 3.00 s? (Indicate the direction with the sign of your answer.)
m/s^2

(b) What is the object's acceleration (in m/s^2) between 3.00 s and 8.00 s? (Indicate the direction with the sign of your answer.)
m/s^2

(c) What is the object's acceleration (in m/s^2) between 13.0 s and 18.0 s? (Indicate the direction with the sign of your answer.)
m/s^2

(d) At what time(s) (in s) is the object moving with the lowest speed? (If there is more than one time, enter the times from smallest to largest. If there is only one time, enter 0 in the second box.)
s (smaller value)
s (larger value)

(e) At what time (in s) is the object farthest from x = 0?
s

(f) What is the final position x (in m) of the object at t = 18 s?
m

(g) Through what total distance (in m) has the object moved between t = 0 and t = 18 s?
m

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The velocity of a box traveling along the axis is shown as a function of time in the figure below. If the box is at x = 0 when t = 0, answer the following.

vx (m/s)
20
10
0
-10
5 10 15 t (s)

(a) What is the object's acceleration (in m/s^2) between 0 and 3.00 s? (Indicate the direction with the sign of your answer.)
m/s^2

(b) What is the object's acceleration (in m/s^2) between 3.00 s and 8.00 s? (Indicate the direction with the sign of your answer.)
m/s^2

(c) What is the object's acceleration (in m/s^2) between 13.0 s and 18.0 s? (Indicate the direction with the sign of your answer.)
m/s^2

(d) At what time(s) (in s) is the object moving with the lowest speed? (If there is more than one time, enter the times from smallest to largest. If there is only one time, enter 0 in the second box.)
s (smaller value)
s (larger value)

(e) At what time (in s) is the object farthest from x = 0?
s

(f) What is the final position x (in m) of the object at t = 18 s?
m

(g) Through what total distance (in m) has the object moved between t = 0 and t = 18 s?
m

Added by Alex B.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Emily Anderson

01/16/2023

Step 1

- At \( t = 0 \) s, \( v_x = 10 \) m/s. - At \( t = 3 \) s, \( v_x = 0 \) m/s. - At \( t = 8 \) s, \( v_x = 20 \) m/s. - At \( t = 13 \) s, \( v_x = 20 \) m/s. - At \( t = 18 \) s, \( v_x = -10 \) m/s. Show more…

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The velocity of a box traveling along the axis is shown as a function of time in the figure below. If the box is at x = 0 when t = 0, answer the following: (a) What is the object's acceleration (in m/s^2) between 0 and 3.00 s? (Indicate the direction with the sign of your answer.) m/s^2 (b) What is the object's acceleration (in m/s^2) between 3.00 s and 8.00 s? (Indicate the direction with the sign of your answer.) m/s^2 (c) What is the object's acceleration (in m/s^2) between 13.0 s and 18.0 s? (Indicate the direction with the sign of your answer.) m/s^2 (d) At what time(s) (in s) is the object moving with the lowest speed? (If there is more than one time, enter the times from smallest to largest. If there is only one time, enter 0 in the second box.) s (smaller value) s (larger value) (e) At what time (in s) is the object farthest from x = 0? s (f) What is the final position x (in m) of the object at t = 18 s? m (g) Through what total distance (in m) has the object moved between t = 0 and t = 18 s? m

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Transcript

00:01 In this example, we're going to be looking at a velocity versus time graph for an object, and we're going to be asking several questions about this object's motion.

00:13 The graph that we're working with is the following, where we have time in seconds on the x -axis.

00:21 So we'll say time, time in seconds.

00:25 And then on the y -axis, we have velocity in meters per second.

00:32 Okay, so this goes from negative 10 to positive 10.

00:37 Then we start at time t equals zero.

00:42 The first question is we want to know the object's acceleration from t equals zero to three seconds.

00:50 Okay, so from zero to three seconds, we see that we're moving at constant velocity.

00:55 So acceleration equals zero.

00:59 Next, we want to find the acceleration from t equals three to eight seconds.

01:07 Okay, so that's going to be this segment here, three to eight seconds.

01:11 So we know that's just going to be the slope of the velocity curve.

01:16 Okay, so we go from negative nine meters per second to 11 meters per second.

01:24 Okay, so we go positive 20.

01:26 20 divided by we go from 3 seconds to 8 seconds, 5 seconds.

01:32 So the acceleration is 4 meters per second squared.

01:39 Next we want acceleration between 13 and 18 seconds.

01:47 So a4t equals 13 through 18 seconds.

01:55 So that's that segment from 13 to 18 seconds where we stop.

02:02 Again, the acceleration is going to be the slope of that line.

02:05 So we go from 11 to 0 meters per second in a time of five seconds.

02:14 So that's going to be 11, negative 11, over 5 equals 2 .2 meters per second squared.

02:24 And that's negative.

02:27 Next we want to find the times at which the object has the lowest speed.

02:34 Okay, so times where v equals zero...

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