The relation between time and |RECTILINEARMOTIONJEEMAIN2023

JEE MAINS 2024

31.01.24

Question

$$ \text { The relation between time ' } t \text { ' and distance ' } x \text { ' is } t=\alpha x^2+\beta x \text {, where } \alpha \text { and } \beta \text { are constants. The } $$ $$ \text { relation between acceleration (a) and velocity (v) is: } $$

Select the correct option:

$a=-2 \alpha v^3$

$a=-5 \alpha v^5$

$a=-3 \alpha v^2$

$a=-4 \alpha v^4$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Sol. $t=\alpha x^2+\beta x$ (differentiating wrt time) $$ \begin{aligned} & \frac{\mathrm{dt}}{\mathrm{dx}}=2 \alpha \mathrm{x}+\beta \\ & \frac{1}{\mathrm{v}}=2 \alpha \mathrm{x}+\beta \end{aligned} $$ (differentiating wort time) $$ \begin{aligned} & -\frac{1}{\mathrm{v}^2} \frac{\mathrm{dv}}{\mathrm{dt}}=2 \alpha \frac{\mathrm{dx}}{\mathrm{dt}} \\ & \frac{\mathrm{dv}}{\mathrm{dt}}=-2 \alpha \mathrm{v}^3 \end{aligned} $$

Question Tags

JEE Main

Physics

Hard

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