Question

The given figure shows the $v-t$ graph of a particle moving in a straight line. At time $t$ it returns to the starting point. Find $t$. (Assume SI units for the graph)

• A. $45s$
• B. $25s$
• C. $10s$
• D. $40s$

Answer 1

The correct option is A $45s$

As we know that, when the particle comes to initial position, total displacement is zero.
Also, the area of v-t graph gives displacement, in this case, net area of $v-t$ graph should be zero.

$\therefore S=\frac{1}{2}\times 25\times 20-\frac{1}{2}(t-25)\times 25$
or, $0=250-\frac{25}{2}(t-25)$
$\Rightarrow 500=25(t-25)$
$\Rightarrow t-25=20\Rightarrow t=45s$