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The displacement of a body is given to be proportional to the cube of time elapsed. The magnitude of the acceleration of the body is
- a)increasing with time
- b)decreasing with time
- c)constant but not zero
- d)zero
Correct answer is option 'A'. Can you explain this answer?
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The displacement of a body is given to be proportional to the cube of ...
As x ∝ t3
velocity, v ∝ 3t2
Acceleration, a ∝ 6t
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The displacement of a body is given to be proportional to the cube of ...
**Answer:**
The displacement of a body is given to be proportional to the cube of time elapsed. Mathematically, we can represent this relationship as:
d ∝ t^3
where d is the displacement and t is the time elapsed.
To find the magnitude of acceleration, we need to differentiate the displacement equation with respect to time:
a = d^2/dt^2
Since the displacement is proportional to t^3, we can rewrite it as:
d = kt^3
where k is a constant of proportionality.
Differentiating both sides of the equation with respect to time, we get:
a = 3kt^2
This equation shows that the magnitude of acceleration is directly proportional to t^2. As time increases, the magnitude of acceleration also increases.
Therefore, the correct answer is option 'A': the magnitude of acceleration is increasing with time.
The displacement of a body is given to be proportional to the cube of time elapsed. Mathematically, we can represent this relationship as:
d ∝ t^3
where d is the displacement and t is the time elapsed.
To find the magnitude of acceleration, we need to differentiate the displacement equation with respect to time:
a = d^2/dt^2
Since the displacement is proportional to t^3, we can rewrite it as:
d = kt^3
where k is a constant of proportionality.
Differentiating both sides of the equation with respect to time, we get:
a = 3kt^2
This equation shows that the magnitude of acceleration is directly proportional to t^2. As time increases, the magnitude of acceleration also increases.
Therefore, the correct answer is option 'A': the magnitude of acceleration is increasing with time.
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The displacement of a body is given to be proportional to the cube of time elapsed. The magnitude of the acceleration of the body isa)increasing with timeb)decreasing with timec)constant but not zerod)zeroCorrect answer is option 'A'. Can you explain this answer?
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