Understanding Distance-Time Graphs for Constant Speed

A distance-time graph is a way to visualize the motion of an object. It plots the distance covered by the object on the vertical axis (y-axis) against the time taken on the horizontal axis (x-axis).

What is Constant Speed?

Constant speed, also known as uniform speed, means that an object covers equal distances in equal intervals of time. For example, if an object travels 10 meters every second, it is moving with a constant speed of 10 m/s.

Shape of the Graph for Constant Speed

When an object moves with constant speed, the relationship between the distance traveled ($\(d\)$) and the time taken ($\(t\)$) is linear. The distance is directly proportional to time:

$\(d = v \times t\)$

where $\(v\)$ is the constant speed.

In a distance-time graph, this linear relationship results in a straight line.

• If the object starts from rest (distance = 0 at time = 0), the straight line will pass through the origin (0,0).
• If the object has already covered some distance at time = 0, the straight line will start from that initial distance value on the y-axis.

Analyzing the Options

• Curved line: A curved line on a distance-time graph represents non-uniform speed. This means the object's speed is changing, either increasing (acceleration) or decreasing (deceleration).
• Straight line: As explained above, a straight line on a distance-time graph represents constant speed. The slope of the straight line gives the value of the constant speed. A steeper slope indicates higher constant speed, and a less steep slope indicates lower constant speed.
• Line parallel to X axis: A line parallel to the time axis (X-axis) means that the distance is not changing over time. This represents an object that is stationary or at rest.
• Line parallel to Y axis: A line parallel to the distance axis (Y-axis) would mean that the distance changes infinitely in no time. This represents infinite speed, which is physically impossible for any real object.

Therefore, for an object moving with a constant speed, the distance-time graph will be a straight line.