Question

The velocity-time graph for an object is given below. Find the total displacement for the duration of $16\text{s}$?

• A. $100\text{m}$
• B. $120\text{m}$
• C. $80\text{m}$
• D. $90\text{m}$

Answer 1

The correct option is A $100\text{m}$


We know, the area under the velocity - time graph gives displacement.
Let the total displacement $d=d_1+d_2+d_3+d_4$ where,
$d_1$ is the displacement from $0s$ to $2s$.
$d_2$ is the displacement from $2s$ to $10s$.
$d_3$ is the displacement from $10s$ to $12s$.
$d_4$ is the displacement from $12s$ to $16s$.

From the graph, displacement from $0s$ to $2s$,
$d_1=$ Area of triangle
$d_1=\frac{1}{2}\times 2\times 8=8m$
From the graph, displacement from $2s$ to $10s$,
$d_2=$ Area of square
$d_2=8\times 8=64m$
From the graph, displacement from $10s$ to $12s$,
$d_3=$ Area of triangle + Area of rectangle
$d_3=(\frac{1}{2}\times 4\times 2)+(4\times 2)$
$=4+8=12m$
From the graph, displacement from $12s$ to $16s$,
$d_4=$ Area of square
$d_4=4\times 4=16m$

Total displacement:
$d=d_1+d_2+d_3+d_4$
$\Rightarrow$$d=8+64+12+16=100m$