An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by:
An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by:
Option 1 -
(8P/9m)¹/² t³/²
Option 2 -
(8P/9)¹/² t³/²
Option 3 -
(9m/8P)¹/² t³/²
Option 4 -
(9m/8P)¹/² t³/²
Asked by Shiksha User
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1 Answer
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Correct Option - 4
Detailed Solution:P = Fv = (ma)v = m (dv/dt)v
P dt = mv dv
∫P dt = ∫mv dv
Pt = ½mv²
v = √ (2Pt/m)
dx/dt = √ (2P/m) t¹/²
x = √ (2P/m) ∫t¹/² dt = √ (2P/m) * (2/3)t³/²
Squaring to match options:
x² = (8P/9m) t³
This does not match. Let's re-examine the options.
Position x is proportional to t³/².
x = (8P/9m)¹/² t³/²
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