Question

The displacement-time graph for two particles A and B are straight lines inclined at angles of 30° and 45° with the time axis. The ratio of the velocities of A:B is.

Answer 1

Velocity = Slope of the line formed in displacement v/s time graph = Tanθ
Va : Vb = Tan30 : Tan45 = (1/√3) : 1 = 1 : √3

Ratio of velocities of A:B is 1 : √3

Answer 2

Answer:

The ratio of velocities of A:B is $\bold{{\text {Velocity of } B}=1 : \sqrt{3}}}$

Explanation:

The two particles moves with different velocities acquiring two different slopes in displacement time graph. The velocity ratio of both will be calculated by knowing their velocity through –

Given that angle of inclination for particle A = 30 degree

Angle of inclination for particle B = 45 degree

Slope of the displacement time graph gives the velocity

Therefore, slope of A = velocity of A and slope of B = velocity of B  

Slope of A = velocity of A

Slope of A = $\tan \theta$  

Velocity of A = $\tan \theta$

Velocity of A = tan 30

Slope Of B = velocity of B

Slope of B = $\tan \theta$

Velocity of B = tan 45

$\begin{array}{c}\bold{{\text {Ratio of velocity}=\frac{\text {Velocity} \text { of } A}{\text {Velocity} \text { of } B}}} \\ {\frac{\text { Velocity of } A}{\text {Velocity of } B}=\frac{\tan 30}{\tan 45}}\end{array}$

$\frac{\text {Velocity of } A}{\text {Velocity of } B}=\frac{\frac{1}{\sqrt{3}}}{1}$

$\begin{array}{c}{\frac{\text {Velocity} \text { of } A}{\text {Velocity} \text { of } B}=\frac{1}{\sqrt{3}}} \\ {\frac{\text {Velocity of } A}{\text {Velocity of } B}=\bold{1 : \sqrt{3}}\end{array}}$