Question

Figure shows the speed-time graph of a particle. Find the distance travelled in the time interval $0$ to $40\text{s}$.

• A. $300\text{m}$
• B. $400\text{m}$
• C. $500\text{m}$
• D. $600\text{m}$

Answer 1

The correct option is A $300\text{m}$

The distance travelled is equal to the area under the graph.
This area is equal to the area of the triangle OAE + the area of the rectangle ABDE + the area of the triangle BCD.

The area of the triangle OAE is
$A_1=\frac{1}{2}\times OA\times AE=\frac{1}{2}\times \left(10\right)\times \left(10\right)=50\text{m}.$
The area of the rectangle ABDE is
$A_2=AE\times AB=\left(10\right)\times \left(20\right)=200\text{m}$
The area of the triangle BCD is
$A_3=\frac{1}{2}\times BC\times BD=\frac{1}{2}\times \left(10\right)\times \left(10\right)=50\text{m}.$
The total area is $A_1+A_2+A_3=50\text{m}+200\text{m}+50\text{m}=300\text{m}$
The total distance covered is $300\text{m}$.