Question

An object has the acceleration - time graph as shown in figure. When does the object return to its initial velocity?

• A. At $t=4\text{s}$
• B. At $t=7\text{s}$
• C. At $t=8\text{s}$
• D. Impossible to determine from the given information

Answer 1

The correct option is B At $t=7\text{s}$

From $t=0$ to $t=4\text{s}$
Area under the $a-t$ graph is given by
$A_1=-(1.5\times 4)=-6\text{m/s}$
Let the particle attain initial velocity again after time $t^{\prime }$
So, from $t=4\text{s}$ to $t=t^{\prime }\text{s}$
Area under the $a-t$ graph is given by
$A_2=2t^{\prime }$
We know that area under the $a-t$ graph represents change in velocity.
As the initial and final velocities are same,
$\Delta v=0$ (where $\Delta v$ is change in velocity)
$\Rightarrow A_1+A_2=0$
$\Rightarrow -6+2t^{\prime }=0$
$\Rightarrow t^{\prime }=3\text{s}$
So, the desired time $=4+3=7\text{s}$
Hence, the correct answer is option (b)