Question

The variation in velocity of a particle moving along a straight line is shown in the figure. If the particle is moving along x-axis with initial position $x=10\text{m}$, find the final position of particle.

• A. $35\text{m}$
• B. $25\text{m}$
• C. $45\text{m}$
• D. $55\text{m}$

Answer 1

The correct option is A $35\text{m}$

For finding displacement, area below the time axis is considered with $-ve$ sign, due to velocity in opposite direction.
Initial position, $x_i=10\text{m}$

$\text{Displacement (S)}=\text{area under}(v-t)\text{graph}$
$S=$Area of trapezium$-$Area of triangle
$\Rightarrow S=[\frac{1}{2}\times (4+10)\times 5]-[\frac{1}{2}\times 4\times 5]$
$\therefore S=25\text{m}$
In terms of position $x$, displacement is given as:
$S=x_f-x_i$
$\therefore x_f=x_i+25=10+25=35\text{m}$