Concept explainers
A particle moves in a straight line with the velocity shown in the figure. Knowing that x = −540 m at t = 0, (a) construct the a−t and x−t curves for 0 < t < 50 s, and determine (b) the maximum value of the position coordinate of the particle, (c) the values of t for which the particle is at x = 100 m.
Fig. P11.63 and P11.64
(a)
Construct the
Explanation of Solution
Given information:
The position
Calculation:
Show v-t curve of particle that moves in a straight line as in Figure (1).
Calculate the acceleration
Refer Figure (1), the slope of the v-t curve is constant from 0 sec to 10 sec. Hence, the acceleration
Calculate the acceleration
Here,
Substitute
Calculate the acceleration
Refer Figure (1), the slope of the v-t curve is constant from 26 sec to 41 sec. Hence, the acceleration
Calculate the acceleration
Here,
Substitute
Calculate the acceleration
Refer Figure (1), the slope of the v-t curve is constant from 46 to end of the graph. Hence the acceleration
Tabulated the acceleration (a) corresponding to time (t) as in Table 1:
t (sec) | |
0 | 0 |
10 | –5 |
26 | 0 |
41 | 3 |
46 | 0 |
Plot the a-t curve of the motion of the particle as in Figure (2).
Calculate the position
Here,
Substitute
Calculate the time
Here, v is final velocity of particle,
Substitute 10s for
Calculate the position
Substitute
Calculate the position
Here,
Substitute
Calculate the position
Here,
Substitute
Calculate the position
Here,
Substitute
Calculate the position
Here,
Substitute
Tabulated the position (x) corresponding to time (t) as in Table 2:
t (s) | x(m) |
0 | –540 |
10 | 60 |
22 | 420 |
26 | 380 |
41 | 80 |
46 | 17.5 |
50 | –2.5 |
Plot the x-t curve of particle that moves in a straight line with areas as in Figure (3).
(b)
The maximum value of position coordinate
Answer to Problem 11.64P
The maximum value of position coordinate
Explanation of Solution
Given information:
The position
Calculation:
Refer Figure (3) for maximum value of position coordinate
Therefore, the maximum value of position coordinate
(c)
The value of
Answer to Problem 11.64P
The value of
Explanation of Solution
Given information:
The position
Calculation:
Show the v-t curve between 10 to 22 sec in Figure (4).
Calculate velocity
Substitute
Calculate the time
Substitute
Solve the above quadratic equation for the roots:
The roots
Show the x-t curve between 26 sec to 41 sec in Figure (5).
Calculate time
Here,
Substitute
Therefore, the value of
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Chapter 11 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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