Concept explainers
The motion of a particle is defined by the equations
(a)
The magnitudes of the smallest and largest velocities reached by the particle.
Answer to Problem 11.92P
Explanation of Solution
Given information:
The motion of a particle is defined by the equation,
Where x and y is expressed in feet and t is in seconds.
Sketch the path of the particle as plotted y versus x in the graph.
By using the equation of x and y the value is obtained and shown in the table below:
The graph between x and y.
The velocity versus time curve.
We can obtain the velocity (v) at any time (t) by differentiating (x) with respect to (t),
Since,
And,
Now, velocity:
Again, differentiating the above value of v2 with respect to t:
When
Then,
When
Then,
(b)
The corresponding times, positions and directions of the velocities.
Answer to Problem 11.92P
Explanation of Solution
Given information:
The motion of a particle is defined by the equation,
Where x and y is expressed in feet and t is in seconds.
We can obtain the velocity (v) at any time (t) by differentiating (x) with respect to (t),
Since,
And,
Now, velocity
Again differentiating the above value of v2 with respect to t:
When
When N=0, 1, 2............
Then the position of particle at x and y;
And velocities:
When
When N=0, 1, 2............
Then the position of particle at x and y;
And velocities:
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Chapter 11 Solutions
Vector Mechanics for Engineers: Dynamics
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