Question

For the displacement-time graph shown in figure, the ratio of the magnitudes of the instantaneous velocities during $t=1\text{s}$ and $t=4\text{s}$ is

• A. 1 : 1
• B. 2 : 1
• C. 1 : 2
• D. 3 : 2

Answer 1

The correct option is B 2 : 1

Slope of displacement-time graph at a point represents instantaneous velocity.
$\therefore$Velocity at $t=1\text{sec}$ is given by
$v_1=\frac{dx}{dt}=\text{tan}\theta =\frac{20}{2}\text{m/s}$
Velocity at $t=4\text{sec}$ is given by
$v_2=\frac{dx}{dt}=\text{tan}\theta =-\frac{20}{4}\text{m/s}$
($\because$ direction gets reversed)
$\Rightarrow$ Ratio of magnitudes of velocities $=\frac{v_1}{v_2}=\frac{10}{5}=2:1$