A particle has the following position vector æ(t) = at³ + (t + to)? * Find the velocity and the acceleration of the particle as a function of time where a, Y, and to are positive constants.

University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter3: Motion Along A Straight Line
Section: Chapter Questions
Problem 113CP: The position of a particle moving along the x -axis varies with time according to x(t)=5.0t24.0t3 ....
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A particle has the following position vector
x(t) = at³ +
(t + to) "
Find the velocity and the acceleration of the particle as a function of time where
a, y, and to are positive constants.
v(t)
2at?
2y
6y
a(t) = 3at +
-
(t + to)³
(t +to)4
2y
6y
v(t) = 2at³
a(t)
(t + to)3'
= 6at +
-
(t + to)³
27
v(t) = 3at² +
(t + to)3
2y
a(t) :
2at +
(t +to)4
2y
6y
v(t) = 3at²
+
(t + to) "
a(t) = 6at
(t + to)ª
27
6y
v(t) = 3at?
a(t)
(t + to)3
= 6at +
-
(t + to)4
Transcribed Image Text:A particle has the following position vector x(t) = at³ + (t + to) " Find the velocity and the acceleration of the particle as a function of time where a, y, and to are positive constants. v(t) 2at? 2y 6y a(t) = 3at + - (t + to)³ (t +to)4 2y 6y v(t) = 2at³ a(t) (t + to)3' = 6at + - (t + to)³ 27 v(t) = 3at² + (t + to)3 2y a(t) : 2at + (t +to)4 2y 6y v(t) = 3at² + (t + to) " a(t) = 6at (t + to)ª 27 6y v(t) = 3at? a(t) (t + to)3 = 6at + - (t + to)4
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