Concept explainers
A particle moves in a straight line with a constant acceleration of −4 ft/s2 for 6 s, zero acceleration for the next 4 s, and a constant acceleration of +4 ft/s2 for the next 4 s. Knowing that the particle starts from the origin and that its velocity is −8 ft/s during the zero acceleration time interval, (a) construct the v−t and x−t curves for 0 ≤ t ≤ 14 s, (b) determine the position and the velocity of the particle and the total distance traveled when t = 14 s.
Fig. P11.61 and P11.62
(a)
Construct the
Explanation of Solution
Given information:
The constant acceleration
The acceleration is zero from 6sec to 10 sec.
From 10 sec to 14 sec the acceleration
The velocity
Calculation:
Show a-t curve of particle that moves in a straight line as in Figure (1).
Calculate the area
Substitute 6 sec for
Calculate the area
Substitute 4 sec for
Calculate the velocity
Substitute
Calculate the velocity
Substitute
Calculate the velocity
Substitute
Tabulated the acceleration (a), velocity (v) corresponding to time (t) in Table (1) :
t(s) | ||
0 | -4 | 16 |
6 | 0 | -8 |
10 | 0 | -8 |
14 | 4 | 8 |
Plot the v-t curve of particle that moves in a straight line with areas as in Figure (2).
Calculate the area
Here,
Substitute 4 sec for
Calculate the area
Here,
Substitute 2 sec for
Calculate the area
Here,
Substitute 4 sec for
Calculate the area
Here,
Substitute 2 sec for
Calculate the area
Here,
Substitute 4 sec for
Calculate the position
Calculate the position
Substitute 0 for
Calculate the position
Substitute
Calculate the position
Substitute
Calculate the position
Substitute
Calculate the position
Substitute
Tabulated the position (x) corresponding to time (t) in Table 2:
t (sec) | x (ft) |
0 | 0 |
4 | 32 |
6 | 24 |
10 | -8 |
12 | -16 |
14 | -8 |
Plot x-t curve of particle that moves in a straight line with areas as in Figure 3.
(b)
The position, velocity of the particle and the total distance (d) traveled when time (t) 14 sec.
Answer to Problem 11.61P
The total distance (d) traveled when time (t) 14 sec is
Explanation of Solution
Given information:
The constant acceleration
The acceleration is zero from 6sec to 10 sec.
From 10 sec to 14 sec the acceleration
The velocity
Calculation:
Calculate the area
Substitute 6 sec for
Calculate the area
Substitute 4 sec for
Calculate the velocity
Substitute
Calculate the velocity
Substitute
Calculate the velocity
Substitute
Calculate the area
Here,
Substitute 4 sec for
Calculate the area
Here,
Substitute 2 sec for
Calculate the area
Here,
Substitute 4 sec for
Calculate the area
Here,
Substitute 2 sec for
Calculate the area
Here,
Substitute 4 sec for
Calculate the position
Calculate the position
Substitute 0 for
Calculate the position
Substitute
Calculate the position
Substitute
Calculate the position
Substitute
Calculate the position
Substitute
Calculate the distance
Substitute 0 for
Calculate the distance
Substitute
Calculate the distance
Substitute
Calculate the total distance (d) traveled when time (t) is 14 sec
Substitute
Therefore, the total distance (d) traveled when time (t) 14 sec is
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Chapter 11 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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