Question

The motion of an airplane is represented by the velocity-time graph as shown below. The distance covered by the airplane in the first 30.5 seconds is                km.

• A. 9
• B. 6
• C. 3
• D. 12

Hint:

To find the distance covered by an object when given a velocity-time graph, calculate the area under the curve. If the graph is a combination of shapes like rectangles and triangles, calculate each area separately and then add them up.

Answer 1

The Correct Option is D

To determine the distance covered by the airplane in the first 30.5 seconds using the velocity-time graph, follow these steps:

Step 1: Understand the Graph

The x-axis represents time (seconds).

The y-axis represents velocity (km/s).

The area under the velocity-time graph gives the distance traveled.

Step 2: Identify the Shape of the Graph

The graph forms a right triangle from 0 to 30.5 seconds.

The base (b) of the triangle = 30.5 seconds.

The height (h) of the triangle = 0.8 km/s.

Step 3: Calculate the Area of the Triangle

The area A of a right triangle is given by:

\( A = \frac{1}{2} \times \text{base} \times \text{height} \)

Substituting the values:

\( A = \frac{1}{2} \times 30.5 \times 0.8 \)

\( A = \frac{1}{2} \times 24.4 \)

\( A = 12.2 \) km