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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?
Most Upvoted Answer
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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