The displacement-time graphs of two moving particles make angles of 30° and 45° with the time X -axis The ratio of their velocities is

Question

The displacement-time graphs of two moving particles make angles of 30° and 45° with the time X -axis The ratio of their velocities is (A) √3:2 (B) 1: 1 (C) 1: 2 (D) 1:√3

Tardigrade Admin · Accepted Answer

By the definition, the slope of displacement-time graph is velocity. i.e., v= tan θ ∴ (v1/v2)=( tan θ1/ tan θ2) (v1/v2)=( tan 30°/ tan 45°) (v1/v2)=(1/√3)

Q. The displacement-time graphs of two moving particles make angles of $3 0^{\circ}$ and $4 5^{\circ}$ with the time $X$ -axis The ratio of their velocities is

$3 : 2$

$1 : 1$

$1 : 2$

$1 : 3$

By the definition, the slope of displacement-time graph is velocity.
i.e., $v = tan θ$
$∴ \frac{v _{1}}{v _{2}} = \frac{t a n θ _{1}}{t a n θ _{2}}$
$\frac{v _{1}}{v _{2}} = \frac{t a n 3 0 ^{\circ}}{t a n 4 5 ^{\circ}}$
$\frac{v _{1}}{v _{2}} = \frac{1}{3}$

Q. The displacement-time graphs of two moving particles make angles of 30∘ and 45∘ with the time X -axis The ratio of their velocities is

3​:2

1:1

1:2

1:3​