Question

The acceleration versus time graph for a particle moving along a straight line is shown in the figure. If the particle starts from rest at $t=0$, then its speed at $t=30\text{s}$ will be

• A. $20\text{m/s}$
• B. $0\text{m/s}$
• C. $-40\text{m/s}$
• D. $60\text{m/s}$

Answer 1

The correct option is C $-40\text{m/s}$

For $a-t$ curve,
area under the graph = change in velocity.

Total area under the graph from $t=0$ to $t=30\text{s}$ is given by
$A$= Area of the graph from $t=0$ to $t=10\text{s}$ + Area of the graph from $t=10\text{s}$ to $t=30\text{s}$
$\Rightarrow A=4\times 10-20\times 4=-40\text{m/s}$
Now,
$A=\Delta v$ (where $\Delta v$ is change in velocity)
$\Rightarrow -40=v_{30}-v_0$
As $v_0=0$
$\therefore v_{30}=-40\text{m/s}$
Hence, speed of the particle at $30\text{s}=-40\text{m/s}$