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The displacement of particle is given by y=a +bt +ct^2-dt^4.initial velocity and acceleration?? ans- -b. and 2c respectively..?
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The displacement of particle is given by y=a +bt +ct^2-dt^4.initial ve...
For velocity diff. it and for acceleration double differentiation of displacement is done..
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The displacement of particle is given by y=a +bt +ct^2-dt^4.initial ve...
Given information:
The displacement of a particle is given by the equation y = at + bt^2 + ct^2 - dt^4.
To find:
We need to determine the initial velocity and acceleration of the particle.
Solution:
Step 1: Differentiate the displacement equation to find velocity:
To find the velocity of the particle, we need to differentiate the displacement equation with respect to time (t).
Differentiating the equation y = at + bt^2 + ct^2 - dt^4 with respect to t, we get:
dy/dt = a + 2bt + 2ct - 4dt^3
This represents the velocity of the particle at any given time.
Step 2: Finding initial velocity:
The initial velocity of the particle is the velocity at time t = 0. Substituting t = 0 into the velocity equation, we get:
dy/dt = a + 2b(0) + 2c(0) - 4d(0)^3
dy/dt = a
Therefore, the initial velocity of the particle is a.
Step 3: Differentiate the displacement equation again to find acceleration:
To find the acceleration of the particle, we need to differentiate the displacement equation (y = at + bt^2 + ct^2 - dt^4) again with respect to time (t).
Differentiating the velocity equation (dy/dt = a + 2bt + 2ct - 4dt^3) with respect to t, we get:
d^2y/dt^2 = 2b + 2c - 12dt^2
This represents the acceleration of the particle at any given time.
Step 4: Finding initial acceleration:
The initial acceleration of the particle is the acceleration at time t = 0. Substituting t = 0 into the acceleration equation, we get:
d^2y/dt^2 = 2b + 2c - 12d(0)^2
d^2y/dt^2 = 2b + 2c
Therefore, the initial acceleration of the particle is 2b + 2c.
Final Answer:
The initial velocity of the particle is -b and the initial acceleration is 2c.
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The displacement of particle is given by y=a +bt +ct^2-dt^4.initial velocity and acceleration?? ans- -b. and 2c respectively..?
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The displacement of particle is given by y=a +bt +ct^2-dt^4.initial velocity and acceleration?? ans- -b. and 2c respectively..? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The displacement of particle is given by y=a +bt +ct^2-dt^4.initial velocity and acceleration?? ans- -b. and 2c respectively..? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The displacement of particle is given by y=a +bt +ct^2-dt^4.initial velocity and acceleration?? ans- -b. and 2c respectively..?.
The displacement of particle is given by y=a +bt +ct^2-dt^4.initial velocity and acceleration?? ans- -b. and 2c respectively..? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The displacement of particle is given by y=a +bt +ct^2-dt^4.initial velocity and acceleration?? ans- -b. and 2c respectively..? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The displacement of particle is given by y=a +bt +ct^2-dt^4.initial velocity and acceleration?? ans- -b. and 2c respectively..?.
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