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The motion of a particle along a straight line is described by equation x = 8 + 12t − t3 where x is in metre and t in second. The retardation of the particle when its velocity becomes zero is
- a)24ms−2
- b)zero
- c)6ms−2
- d)12ms−2
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
The motion of a particle along a straight line is described by equati...
Given : x = 8 + 12t − t3
When v = 0, 12 − 3t2 = 0 or t = 2s
a t =2s = −12ms−2
Retardation = 12ms−2
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The motion of a particle along a straight line is described by equati...
Given Equation:
x = 8 + 12t − t^3
Velocity of the particle:
The velocity of the particle can be determined by differentiating the given equation with respect to time (t).
dx/dt = 12 - 3t^2
Retardation:
The particle will come to a stop when its velocity becomes zero. So, we set the velocity equation equal to zero and solve for t.
12 - 3t^2 = 0
3t^2 = 12
t^2 = 4
t = 2 seconds
Retardation Calculation:
To find the retardation, we need to calculate the acceleration at t = 2 seconds. The acceleration is the derivative of velocity with respect to time.
dv/dt = -6t
Substitute t = 2 seconds into the acceleration equation:
a = -6(2)
a = -12 m/s^2
Therefore, the retardation of the particle when its velocity becomes zero is 12 m/s^2, which is option 'D'.
x = 8 + 12t − t^3
Velocity of the particle:
The velocity of the particle can be determined by differentiating the given equation with respect to time (t).
dx/dt = 12 - 3t^2
Retardation:
The particle will come to a stop when its velocity becomes zero. So, we set the velocity equation equal to zero and solve for t.
12 - 3t^2 = 0
3t^2 = 12
t^2 = 4
t = 2 seconds
Retardation Calculation:
To find the retardation, we need to calculate the acceleration at t = 2 seconds. The acceleration is the derivative of velocity with respect to time.
dv/dt = -6t
Substitute t = 2 seconds into the acceleration equation:
a = -6(2)
a = -12 m/s^2
Therefore, the retardation of the particle when its velocity becomes zero is 12 m/s^2, which is option 'D'.
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The motion of a particle along a straight line is described by equation x = 8 + 12t − t3 where x is in metre and t in second. The retardation of the particle when its velocity becomes zero isa)24ms−2b)zeroc)6ms−2d)12ms−2Correct answer is option 'D'. Can you explain this answer?
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