Concept explainers
The acceleration of a particle is defined by the relation a = −kv2.5, where k is a constant. The particle starts at x = 0 with a velocity of 16 mm/s, and when x = 6 mm, the velocity is observed to be 4 mm/s. Determine (a) the velocity of the particle when x = 5 mm, (b) the time at which the velocity of the particle is 9 mm/s.
(a)
The velocity (v) of the particle when position (x) is
Answer to Problem 11.25P
The velocity (v) of the particle is
Explanation of Solution
Given information:
The acceleration (a) of the particle is
The initial position
At initial velocity
When the position (x) is
Calculation:
Write the relation for the acceleration (a) as given below:
Here, v is velocity and k is the constant.
Express acceleration (a) by differentiation velocity (v) with respective to position (x) below;
Substitute
Apply integration.
Integrate the equation.
Calculate the value (k).
Substitute
Calculate the velocity (v) when the position (x) is
Substitute
Therefore, the velocity (v) of the particle is
(b)
The time (t) at which the velocity (v) of the particle is
Answer to Problem 11.25P
The time (t) at which the velocity (v) of the particle is
Explanation of Solution
Given information:
The acceleration (a) of the particle is
The initial position
At initial velocity
When the position (x) is
Calculation:
Express acceleration (a) by differentiation velocity (v) with respective to time (t) below;
Substitute
Apply integration.
Integrate the equation.
Calculate the time (t) at which the velocity (v) of the particle is
Substitute
Therefore, the time (t) at which the velocity (v) of the particle is
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Chapter 11 Solutions
Connect 2 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics
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