Question

The speed-time graph for a car is shown is Fig.

 

1. Find how far does the car travel in the first 4 seconds. Shade the area on the graph that represents the distance travelled by the car during the period. 
2. Which part of the graph represents uniform motion of the car?

Answer 1

Speed-Time Graph Analysis for a Car 

Given Speed-Time Graph:

1. How far does the car travel in the first 4 seconds?

To find the distance travelled by the car, we use the area under the speed-time graph. The area under the graph represents the distance travelled by the car.

In the first 4 seconds, the graph shows a **triangle** formed by the speed-time coordinates. The area of the triangle can be calculated using the formula:

\[ \text{Area of the triangle} = \frac{1}{2} \times \text{Base} \times \text{Height} \] - Base = 4 seconds (time period) - Height = 10 m/s (speed at the end of 4 seconds) \[ \text{Distance} = \frac{1}{2} \times 4 \, \text{seconds} \times 10 \, \text{m/s} = 20 \, \text{meters} \]

The car travels 20 meters in the first 4 seconds.

2. Which part of the graph represents uniform motion of the car?

Uniform motion is represented by a **horizontal line** on a speed-time graph, indicating constant speed. In this graph, the portion where the speed remains constant (horizontal part) represents uniform motion.

From the graph, this is visible between 6 seconds and 8 seconds, where the speed is constant at 10 m/s.

Summary:

• The car travels 20 meters in the first 4 seconds.
• The uniform motion of the car is represented by the horizontal section of the graph between 6 and 8 seconds.