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The motion of a set of particles moving along the x-axis is governed by the differential equation dx dt = t 3 – x3, where x1t2 denotes the p
Question
The motion of a set of particles moving along the x-axis is governed by the differential equation dx dt = t 3 – x3, where x1t2 denotes the position at time t of the particle. (a) If a particle is located at x = 1 when t = 2, what is its velocity at this time? (b) Show that the acceleration of a particle is
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2021-09-05T08:05:59+00:00
2021-09-05T08:05:59+00:00 1 Answers
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Answers ( )
Answer:
a)V=7 m/s
b)a=3t²-3x² t³ +3 x ⁵
Explanation:
Given that
[tex]\dfrac{dx}{dt}=t^3-x^3[/tex]
a)
We know that velocity V is given as follows
[tex]V=\dfrac{dx}{dt}[/tex]
[tex]V=t^3-x^3[/tex]
At t= 2 s and x= 1 m
[tex]V=2^3-1^3=7 m/s[/tex]
V=7 m/s
b)
Acceleration a is given as follows
[tex]a=\dfrac{dV}{dt}[/tex]
[tex]a=3t^2-3x^2\dfrac{dx}{dt}[/tex]
Now by putting the values
[tex]a=3t^2-3x^2\times (t^3-x^3)[/tex]
a=3t²-3x² t³ +3 x ⁵
Therefore the acceleration of a particle will be 3t²-3x² t³ +3 x ⁵.