
Concept explainers
a. If s = (2t3) m, where t is in seconds, determine v when t = 2 s.
b. If v = (5s) m/s, where s is in meters, determine a at s = 1 m.
c. If v = (4t + 5) m/s, where t is in seconds, determine a when t = 2 s.
d. If a = 2 m/s2, determine v when t = 2 s if v = 0 when t = 0.
e. If a = 2 m/s2, determine v at s= 4 m if v = 3 m/s at s = 0.
f. If a = (s) m/s2, where s is in meters, determine v when s = 5 m if v = 0 at s = 4 m
g. If a = 4 m/s2, determine s when t = 3 s if v = 2 m/s and s = 2 m when t = 0.
h. It a = (8t2) m/s2, determine v when t = 1 s if v = 0 at t = 0.
i. If s = (3t2 + 2) m, determine v when t = 2 s.
j. When t = 0 the particles is at A. In four seconds it travels to B, then in another six seconds it travels to C. Determine the average velocity and the average speed. The origin of the coordinate is at O.
a)

The velocity when time is
Answer to Problem 1PP
The velocity when time is
Explanation of Solution
Given:
The time is
The distance equation is
Write the distance equation.
Here, average velocity is
Write the expression velocity.
Here, velocity is
Conclusion:
Substitute
Substitute
Thus, the velocity when time is
b)

The acceleration when distance
Explanation of Solution
The acceleration
Given:
The distance is
The velocity equation is
Write the velocity equation.
Write the expression acceleration.
Here, velocity is
Conclusion:
Substitute
Substitute
Thus, the acceleration
c)

The acceleration when distance
Answer to Problem 1PP
The acceleration
Explanation of Solution
Given:
The distance is
The velocity equation is
Write the velocity equation.
Write the expression acceleration.
Here, acceleration is
Conclusion:
Substitute
Thus, the acceleration
d)

The velocity when time is
Answer to Problem 1PP
The velocity
Explanation of Solution
Given:
The time is
The acceleration is
The initial velocity is
Write the expression for final velocity in
Here, final velocity is
Conclusion:
Substitute
Thus, the velocity
e)

The velocity when distance is
Answer to Problem 1PP
The velocity
Explanation of Solution
Given:
The time is
The acceleration is
The initial velocity is
The initial distance is
The final distance is
Write the expression for final velocity in
Here, final velocity is
Conclusion:
Substitute
Thus, the velocity
f)

The velocity
Answer to Problem 1PP
The velocity
Explanation of Solution
Given:
The distance is
The distance is
The acceleration equation is
Write the acceleration equation.
Write the expression acceleration.
Here, velocity is
Conclusion:
Substitute
Integrate the Equation (I) at the limits
Thus, the velocity
g)

The distance when time is
Answer to Problem 1PP
The distance
Explanation of Solution
Given:
The time is
The acceleration is
The velocity is
The distance is
Write the expression for final distance in
Here, final distance is
Conclusion:
Substitute
Thus, the distance
h)

The velocity when time is
Answer to Problem 1PP
The velocity
Explanation of Solution
Given:
The time is
The acceleration equation is
Write the acceleration equation.
Write the expression acceleration.
Here, acceleration is
Conclusion:
Substitute
Integrate the Equation (I) at the limits
Substitute
Thus, the velocity when time is
i)

The velocity when time is
Answer to Problem 1PP
The velocity
Explanation of Solution
Given:
The time is
The distance equation is
Write the distance equation.
Here, average velocity is
Write the expression velocity.
Here, velocity is
Conclusion:
Substitute
Substitute
Thus, the velocity
j)

The average velocity and the average speed of the particle.
Answer to Problem 1PP
The average velocity of particle is
The average speed of particle is
Explanation of Solution
Given:
The distance traveled by the particle from
The time traveled by the particle from
The time traveled by the particle from
Write the expression for the average velocity.
Here, average velocity is
Write the expression for the average speed
Here, the total distance is
Refer Figure (1) and calculate the total distance traveled by the particle.
Refer Figure (1) and calculate the total time traveled by the particle.
Conclusion:
From the Figure (1) calculate the change in distance.
Calculate the change in distance
Substitute
Thus, the average velocity of particle is
The time traveled by the particle from
The time traveled by the particle from
Substitute
Substitute
Substitute
Thus, the average speed of particle is
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Chapter 12 Solutions
Engineering Mechanics: Dynamics (14th Edition)
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