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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 is in Sec. The retardation of the particle when it's velocity becomes zero is?
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The motion of a particle along a straight line is described by equati...
Problem: The motion of a particle along a straight line is described by equation x=8+12t-t³ where x is in metre and t is in Sec. The retardation of the particle when its velocity becomes zero is?
Solution:
To find the retardation of the particle, we first need to find the velocity of the particle. We can find the velocity by taking the derivative of the position equation with respect to time.
x = 8 + 12t - t³
v = dx/dt = 12 - 3t²
Setting the velocity to zero, we get:
12 - 3t² = 0
Solving for t, we get:
t = ±2
Since we are interested in the point where the velocity becomes zero, we take the positive value of t, which is t = 2 sec.
To find the retardation, we need to find the acceleration of the particle at t = 2 sec. We can find the acceleration by taking the derivative of the velocity equation with respect to time.
v = 12 - 3t²
a = dv/dt = -6t
Plugging in t = 2 sec, we get:
a = -12 m/s²
Therefore, the retardation of the particle when its velocity becomes zero is -12 m/s². This means that the particle is decelerating at a rate of 12 m/s².
Solution:
To find the retardation of the particle, we first need to find the velocity of the particle. We can find the velocity by taking the derivative of the position equation with respect to time.
x = 8 + 12t - t³
v = dx/dt = 12 - 3t²
Setting the velocity to zero, we get:
12 - 3t² = 0
Solving for t, we get:
t = ±2
Since we are interested in the point where the velocity becomes zero, we take the positive value of t, which is t = 2 sec.
To find the retardation, we need to find the acceleration of the particle at t = 2 sec. We can find the acceleration by taking the derivative of the velocity equation with respect to time.
v = 12 - 3t²
a = dv/dt = -6t
Plugging in t = 2 sec, we get:
a = -12 m/s²
Therefore, the retardation of the particle when its velocity becomes zero is -12 m/s². This means that the particle is decelerating at a rate of 12 m/s².
Community Answer
The motion of a particle along a straight line is described by equati...
Answer:
12 m/s²
Explanation:
x = 8 + 12t – t³ The final velocity of the particle will be zero, because it retarded.
V= 0 + 12 – 3t² = 0 ⇒ 3t² = 12 ⇒ t = 2 sec
Now the retardation a = dv/ dt = 0 – 6t
a [ t= 2] = – 12 m/s²
retardation = 12 m/s²
12 m/s²
Explanation:
x = 8 + 12t – t³ The final velocity of the particle will be zero, because it retarded.
V= 0 + 12 – 3t² = 0 ⇒ 3t² = 12 ⇒ t = 2 sec
Now the retardation a = dv/ dt = 0 – 6t
a [ t= 2] = – 12 m/s²
retardation = 12 m/s²
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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 is in Sec. The retardation of the particle when it's velocity becomes zero is?
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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 is in Sec. The retardation of the particle when it's velocity becomes zero is? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The motion of a particle along a straight line is described by equation x=8+12t-t³ where x is in metre and t is in Sec. The retardation of the particle when it's velocity becomes zero is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The motion of a particle along a straight line is described by equation x=8+12t-t³ where x is in metre and t is in Sec. The retardation of the particle when it's velocity becomes zero is? .
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