First slide

Instantaneous acceleration

Question

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

Moderate

A

sin 25° to sin 50°
B

tan 25° to tan 40°
C

cos 25° to cos 50°
D

tan 25° to tan 50°

Solution

The slope of velocity-time graph gives acceleration,
i.e. $\frac{a_{A}}{a_{B}} = \frac{\tan θ_{1}}{\tan θ_{2}}$
Here, $θ_{1}$ is the angle made by line A with time axis and $θ_{2}$ is the angle made by line B with time axis
$\Rightarrow$ $\frac{a_{A}}{a_{B}} = \frac{\tan 25 °}{\tan 50 °}$

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