Concept explainers
Many car companies are performing research on collision avoidance systems. A small prototype applies engine braking that decelerates the vehicle according to the relationship
(a)
The expression for the velocity as a function of time.
The expression for the position as a function of time.
Answer to Problem 11.12P
The expression for the velocity as a function of time is
The expression for the position as a function of time is
Explanation of Solution
Given information:
The initial velocity is
Write the expression for the deceleration.
Here, the time is
Write the expression for the velocity.
Substitute
Here, the integration constant is
Write the expression for the position.
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The expression for the velocity as a function of time is
The expression for the position as a function of time is
(b)
The distance travelled by the vehicle before stop.
Answer to Problem 11.12P
The distance travelled by the vehicle before stop is
Explanation of Solution
Given information:
The initial velocity is
Write the expression for the distance travelled by the vehicle.
Write the expression for the velocity.
Calculation:
Substitute
Substitute
Conclusion:
The distance travelled by the vehicle before stop is
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Chapter 11 Solutions
Vector Mechanics For Engineers
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