(a) Explanation Given information: The acceleration of particle is a = k t 2 . Calculation: Write the acceleration of the particle in terms of rate of change of velocity: a = d v d t Here, acceleration of particle is a , change in velocity is dv , and change in time is dt . Rewrite the above equation: d v = a d t Integrate the above equation. ∫ v i = − 8 v f = + 8 d v = a ∫ t i = 0 t f = 2 d t (1) Here, initial velocity of the particle is v i , final velocity of the particle is v f , time corresponding to initial velocity of the particle is t i , and time corresponding to final velocity of the particle is t f . Substitute k t 2 for a in Equation (1) and apply integration to find the value of k (b) To determine Write the equations of motion.

Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9781259639272

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 11.1, Problem 11.12P

(a)

To determine

The constant (k).

(b)

To determine

Write the equations of motion.

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Chapter 11.1, Problem 11.11P

Chapter 11.1, Problem 11.13P

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Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

Ch. 11.1 - A bus travels the 100 miles between A and B at 50...Ch. 11.1 - Two cars A and B race each other down a straight...Ch. 11.1 - A snowboarder starts from rest at the top of a...Ch. 11.1 - Prob. 11.2P Ch. 11.1 - Prob. 11.3P Ch. 11.1 - A loaded railroad car is rolling at a constant...Ch. 11.1 - Prob. 11.5P Ch. 11.1 - Prob. 11.6P Ch. 11.1 - A girl operates a radio-controlled model car in a...Ch. 11.1 - The motion of a particle is defined by the...

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The constant ( k ).