Kinematics

JEE Main level, single correct, medium

127 of 308

Question 127 of 308

If t=x+4t=\sqrt{x}+4, then (dxdt)t=4{\left(\dfrac{dx}{dt}\right)}_{t=4} is:

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Answer: (B) Zero

Given that t=x+4t=\sqrt{x}+4
⇒x=(t−4)2=t2−8t+16\Rightarrow x={\left(t-4\right)}^{2}={t}^{2}-8t+16
Differentiating the above equation with respect to time,
⇒dxdt=2t−8\Rightarrow \dfrac{dx}{dt}=2t-8
Putting the value of t=4t=4
⇒dxdt=2×4−8=0\Rightarrow \dfrac{dx}{dt}=2\times 4-8=0

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