Question

The figure shows the $x-t$ plot of a particle in one-dimensional motion. Two different equal intervals of time are shown. Let $v_1$ and $v_2$ be speed in time intervals $1$ and $2$ respectively. Then

• A. $v_1>v_2$
• B. $v_2>v_1$
• C. $v_1=v_2$
• D. Data is insufficient

Answer 1

The correct option is A $v_1>v_2$

We know,

The slope of the $x-t$ graph represents the speed. The average speed of a particle shown in the $x-t$ graph is obtained from its slope in a particular interval of time. So, the higher the slope of the graph, the higher is the average speed.

Now see the graph,

It is clear from the graph that the magnitude of the slope is more in interval-$1$ than in the interval-$2$.

Therefore, the speed of the particle in $2$ will be less than the $1$.

Thus $v_1>v_2$