The displacement-time graphs of two moving particles make angles of 30° and 45° with the x-axis as shown in the figure. The ratio of their respective velocity is :

Question

The displacement-time graphs of two moving particles make angles of 30° and 45° with the x-axis as shown in the figure. The ratio of their respective velocity is : (A) 1: √3 (B) √3: 1 (C) 1: 1 (D) 1: 2

Tardigrade Admin · Accepted Answer

Velocity is slope of x-t graph V =( dx / dt )= tan θ ( V 1/ V 2)=( tan θ1/ tan θ2) =( tan 30°/ tan 45°)=(1/√3)

Q. The displacement-time graphs of two moving particles make angles of $3 0^{\circ}$ and $4 5^{\circ}$ with the $x$ -axis as shown in the figure. The ratio of their respective velocity is :

$1 : 3$

$3 : 1$

$1 : 1$

$1 : 2$

Velocity is slope of $x - t$ graph
$V = \frac{d x}{d t} = tan θ$
$\frac{V _{1}}{V _{2}} = \frac{t a n θ _{1}}{t a n θ _{2}}$
$= \frac{t a n 3 0 ^{\circ}}{t a n 4 5 ^{\circ}} = \frac{1}{3}$

Q. The displacement-time graphs of two moving particles make angles of 30∘ and 45∘ with the x-axis as shown in the figure. The ratio of their respective velocity is :

1:3​

3​:1

1:1

1:2