Question

The velocity-time graph of the objects A and B makes
angles 300 and 600 with the time axis. Find the ratio of
their acceleration.

Answer 1

Answer:

Given:

Velocity time graph has slopes of 30° and 60° with time axis.

To find:

Ratio of acceleration

Concept:

Slope in velocity time graph actually represents the acceleration because the slope denotes the change of velocity with respect to time.

Regarding Acceleration, it's a vector quantity having both directions and magnitude. Since slope is being considered , we are taking average velocity into consideration.

Calculation:

For particle A :

$acc = \tan(30 \degree) = \dfrac{1}{ \sqrt{3} } \: units$

For particle B:

$acc = \tan(60 \degree) = \sqrt{3} \: units$

Required ratio:

$\boxed{ \red{ \large{A:B = 1 : (\sqrt{3} \times \sqrt{3} ) = 1 : 3}}}$

Answer 2

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Question :

The velocity-time graph of the objects A and B makes

angles 300 and 600 with the time axis. Find the ratio of

their acceleration.

Solution :

$\tt{ \purple{ \implies{ {acc}^{n} = \tan(30) \: = \dfrac{1}{ \sqrt{3} } }}}$

$\tt{ \purple{ \implies{ {acc}^{n} = \tan(60) \: = \sqrt{3} }}}$

Ratio = 1:3