Question

A velocity-time graph for a moving object is shown below. What would be the total displacement during time $t=0$ to $t=6\text{s}$?

• A. $10\text{m}$
• B. $20\text{m}$
• C. $30\text{m}$
• D. $40\text{m}$

Answer 1

The correct option is A $10\text{m}$

The total displacement travelled by the object is the area under the $v-t$ graph. Total displacement during $t=0$ to $t=6\text{s}$ is equal to area under the graph $=A_1+A_2+A_3$.

Since area $A_3$ is on the negative side of the graph, the area will be negative hence, the net displacement.
Displacement $=A_1+A_2+A_3$
$A_1=5\times 2$ = 10m
$A_2=\frac{1}{2}\times 5\times (4-2)$ = 5m
$A_3=\frac{1}{2}\times (-5)\times (6-4)$= -5m
Displacement $=10+5–5=10\text{m}$
Therefore, option A is correct.