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A motion of a particle is described by equation:8 +12t- t3, where 'x' is in metre and 't' is in seconds.The retardation of the particle when its velocity becomes zero is?
Verified Answer
A motion of a particle is described by equation:8 +12t- t3, where 'x' ...
x = 8 + 12t − t^3. −−−−(1)
for velocity of the particle we differentiate above eqn w. r. to time t.
so v = dx/dt = 12 − 3t^2. −−−(2)
when velocity v = 0 then 12 − 3t^2 = 0.
or t = 2second.
differentiating eqn (2) once again w.r.t. time, we get,
a = dv/dt = −6t.
the retardation at time t = 2 second is given by,
a = −12 m/s^2.
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Most Upvoted Answer
A motion of a particle is described by equation:8 +12t- t3, where 'x' ...
Given:
The motion of a particle is described by the equation: x = 8 + 12t - t^3, where 'x' is in meters and 't' is in seconds.
To find:
The retardation of the particle when its velocity becomes zero.
Explanation:
To find the retardation of the particle, we need to first find its velocity and then differentiate the velocity equation to find the acceleration. The retardation is the negative value of the acceleration when the velocity becomes zero.
Step 1: Find the velocity:
The velocity of the particle can be found by differentiating the equation for displacement (x) with respect to time (t).
Given: x = 8 + 12t - t^3
Differentiating both sides with respect to time, we get:
v = dx/dt = d/dt(8 + 12t - t^3)
Differentiating each term separately, we get:
v = 0 + 12 - 3t^2
v = 12 - 3t^2
Step 2: Find when the velocity becomes zero:
To find when the velocity becomes zero, we set v = 0 and solve for 't'.
12 - 3t^2 = 0
3t^2 = 12
t^2 = 4
t = ±2
Therefore, the velocity becomes zero at t = 2 and t = -2.
Step 3: Find the acceleration (retardation):
To find the acceleration, we need to differentiate the velocity equation with respect to time.
Given: v = 12 - 3t^2
Differentiating both sides with respect to time, we get:
a = dv/dt = d/dt(12 - 3t^2)
Differentiating each term separately, we get:
a = 0 - 6t
Step 4: Find the retardation:
The retardation is the negative value of the acceleration when the velocity becomes zero.
Substituting t = 2 into the acceleration equation, we get:
a = -6(2)
a = -12 m/s^2
Therefore, the retardation of the particle when its velocity becomes zero is -12 m/s^2.
Summary:
The retardation of the particle when its velocity becomes zero is -12 m/s^2. This is obtained by differentiating the displacement equation to find the velocity, setting the velocity equation equal to zero to find the time when the velocity becomes zero, differentiating the velocity equation to find the acceleration, and finally taking the negative value of the acceleration when the velocity becomes zero.
The motion of a particle is described by the equation: x = 8 + 12t - t^3, where 'x' is in meters and 't' is in seconds.
To find:
The retardation of the particle when its velocity becomes zero.
Explanation:
To find the retardation of the particle, we need to first find its velocity and then differentiate the velocity equation to find the acceleration. The retardation is the negative value of the acceleration when the velocity becomes zero.
Step 1: Find the velocity:
The velocity of the particle can be found by differentiating the equation for displacement (x) with respect to time (t).
Given: x = 8 + 12t - t^3
Differentiating both sides with respect to time, we get:
v = dx/dt = d/dt(8 + 12t - t^3)
Differentiating each term separately, we get:
v = 0 + 12 - 3t^2
v = 12 - 3t^2
Step 2: Find when the velocity becomes zero:
To find when the velocity becomes zero, we set v = 0 and solve for 't'.
12 - 3t^2 = 0
3t^2 = 12
t^2 = 4
t = ±2
Therefore, the velocity becomes zero at t = 2 and t = -2.
Step 3: Find the acceleration (retardation):
To find the acceleration, we need to differentiate the velocity equation with respect to time.
Given: v = 12 - 3t^2
Differentiating both sides with respect to time, we get:
a = dv/dt = d/dt(12 - 3t^2)
Differentiating each term separately, we get:
a = 0 - 6t
Step 4: Find the retardation:
The retardation is the negative value of the acceleration when the velocity becomes zero.
Substituting t = 2 into the acceleration equation, we get:
a = -6(2)
a = -12 m/s^2
Therefore, the retardation of the particle when its velocity becomes zero is -12 m/s^2.
Summary:
The retardation of the particle when its velocity becomes zero is -12 m/s^2. This is obtained by differentiating the displacement equation to find the velocity, setting the velocity equation equal to zero to find the time when the velocity becomes zero, differentiating the velocity equation to find the acceleration, and finally taking the negative value of the acceleration when the velocity becomes zero.
Community Answer
A motion of a particle is described by equation:8 +12t- t3, where 'x' ...
Retardation=12 m/sec2
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A motion of a particle is described by equation:8 +12t- t3, where 'x' is in metre and 't' is in seconds.The retardation of the particle when its velocity becomes zero is?
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A motion of a particle is described by equation:8 +12t- t3, where 'x' is in metre and 't' is in seconds.The retardation of the particle when its velocity becomes zero is? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A motion of a particle is described by equation:8 +12t- t3, where 'x' is in metre and 't' is in seconds.The retardation of the particle when its velocity becomes zero is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A motion of a particle is described by equation:8 +12t- t3, where 'x' is in metre and 't' is in seconds.The retardation of the particle when its velocity becomes zero is?.
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