question_answer

The velocity - time graph for two bodies A and B are shown. Then the acceleration of A and B are in the ratio

A)  \[tan{{25}^{o}}\]to \[tan{{50}^{o}}\]

B)  \[cos{{25}^{o}}\]to \[cos{{50}^{o}}\]

C)  \[\tan {{25}^{o}}\] to \[\tan {{40}^{o}}\]

D)  \[\sin {{25}^{o}}\] to \[\sin {{50}^{o}}\]

Correct Answer: A

Solution :

: As the slope of velocity-time graph gives acceleration, so acceleration \[a=\tan \theta \] \[\therefore \] From given graph,               The acceleration of A is \[{{a}_{A}}=\tan {{25}^{o}}\] and that of B is \[{{a}_{B}}=\tan {{50}^{o}}\] Their corresponding ratio is \[\frac{{{a}_{A}}}{{{a}_{B}}}=\frac{\tan {{25}^{o}}}{\tan {{50}^{o}}}\]