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Motion — Science STD 9 — Question

Gujarat BoardEnglish MediumSTD 9ScienceMotion1 Mark
MCQ
In the following Questions, the Assertion and Reason have been put forward. Read the statements carefully and choose the correct alternative from the following:
Assertion: Equations of motion can when the acceleration is $a = 2t$ where t seconds.
Reason: The slope of a $v-t$ graph with $60^o$ inclination is greater than $30^o$ inclination.
  • ✓
    Both the Assertion and the Reason are correct and the Reason is the correct explanation of the Assertion.
  • B
    The Assertion and the Reason are correct but the Reason is not the correct explanation of the Assertion.
  • C
    Assertion is true but the Reason is false.
  • D
    The statement of the Assertion is false but the Reason is true.
✓

Answer

Correct option: A.
Both the Assertion and the Reason are correct and the Reason is the correct explanation of the Assertion.

The slope of the distance–time graph gives the speed of the object.
For the particale A, the slope of the line is $\tan\theta_1=\tan30=\frac{1}{\sqrt{3}}$
For the particale B, the slope of the line is $\tan\theta_2=\tan60=\sqrt{3}$
Thus, ratio of the velocities, $\frac{\text{V}_{\text{A}}}{\text{V}_{\text{B}}}=\frac{\tan30}{\tan60}=\frac{\frac{1}{\sqrt{3}}}{\sqrt{3}}=\frac{1}3{}$

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