If the displacement of an object is proportional to square of time then object moves with.?
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The object moves with uniform or constant acceleration.
Given,
Let,
Differentiating with respect to time,
We know first derivative of displacement is velocity.
Again differentiating with respect to time,
We know first derivative of velocity is acceleration.
Since k is a constant,
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Object moves with Uniform Acceleration.
EXPLANATION
Displacement is proportional to square of time
⠀⠀⠀⠀⠀⠀⠀⠀⠀s ∝ t²
⠀⠀⠀⠀⠀⠀⠀⠀⠀s = kt²
⠀⠀⠀ , where k is constant of proportionality.
Differentiating Displacement , we get Velocity (v)
⠀⠀⠀⠀⠀⠀⠀ ds/dt = 2kt
Differentiating Velocity , we get Acceleration (a)
⠀⠀⠀⠀⠀⠀ dv/dt = 2k = constant.
ᗇ So, object moves with Constant Acceleration.
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