KCET · Physics · Motion In One Dimension
The displacement-time graph of two moving particles make angles of \(30^{\circ}\) and \(45^{\circ}\) with the \(X\)-axis. The ratio of their velocities is
- A \(\sqrt{3}: 2\)
- B \(1: 1\)
- C \(1: 2\)
- D \(1: \sqrt{3}\)
Answer & Solution
Correct Answer
(D) \(1: \sqrt{3}\)
Step-by-step Solution
Detailed explanation
By the definition, the slope of displacement-time graph is velocity.
i.e., \(\quad v=\tan \theta\)
\(\therefore \frac{v_{1}}{v_{2}}=\frac{\tan \theta_{1}}{\tan \theta_{2}}\)
\(\frac{v_{1}}{v_{2}}=\frac{\tan 30^{\circ}}{\tan 45^{\circ}}\)
\(\frac{v_{1}}{v_{2}}=\frac{1}{\sqrt{3}}\)
i.e., \(\quad v=\tan \theta\)
\(\therefore \frac{v_{1}}{v_{2}}=\frac{\tan \theta_{1}}{\tan \theta_{2}}\)
\(\frac{v_{1}}{v_{2}}=\frac{\tan 30^{\circ}}{\tan 45^{\circ}}\)
\(\frac{v_{1}}{v_{2}}=\frac{1}{\sqrt{3}}\)
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