SATHEE: Kinematics Question 381

Kinematics Question 381

Question: A truck has to carry a load in the shortest time from one station to another station situated at a distance L from the first. It can start up or slowdown at the same acceleration or deceleration what maximum velocity must the truck attain to satisfy this condition?

Options:

A) $\sqrt{L a}$

B) $\sqrt{2 L a}$

C) $\sqrt{3 L a}$

D) $\sqrt{5 L a}$

Show Answer

Answer:

Correct Answer: A

Solution:

Let v be the maximum velocity attained and t the total time of journey. t’ it’s the duration of acceleration and retardation. Then $v = 0 + a t .$
$∴ L= \frac{1}{2} a t {^{'}}^{2} + v (t - 2 t^{'}) + \frac{1}{2} a t {^{'}}^{2}$

$=a {(\frac{v}{a})}^{2} +v (t - \frac{2 v}{a})$

$= \frac{v^{2}}{a} +vt - \frac{2 v^{2}}{a} =vt - \frac{v^{2}}{a}$

$=t= \frac{L}{v} + \frac{v}{a} \Rightarrow \frac{d v}{d t} = 0 ∴ v_{max} = \sqrt{L a}$

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Kinematics Question 381

Question: A truck has to carry a load in the shortest time from one station to another station situated at a distance L from the first. It can start up or slowdown at the same acceleration or deceleration what maximum velocity must the truck attain to satisfy this condition?

Options:

Answer:

Solution:

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