For an object moving with constant (uniform) speed in a straight line, the distance time graph representing its motion is a ______.

Introduction / Context:

Graphs are powerful tools in physics because they show relationships between physical quantities at a glance. A common graph is the distance time graph for an object in motion. Understanding how different types of motion appear on such graphs helps you interpret and solve kinematics problems more quickly. This question asks what the distance time graph looks like when an object moves with constant speed.

Given Data / Assumptions:

• The object is moving along a straight line.
• The speed of the object is constant, meaning it covers equal distances in equal intervals of time.
• The vertical axis of the graph represents distance from a chosen origin, and the horizontal axis represents time.
• No sudden jumps or stops are mentioned; the motion is smooth and uniform.

Concept / Approach:

Distance is related to speed and time by the simple relation distance = speed * time for motion at constant speed starting from zero distance. If speed is constant, distance increases linearly with time, meaning that when time doubles, distance also doubles. Graphically, a linear relationship between two variables appears as a straight line. The slope (gradient) of the line on a distance time graph represents the speed of the object. A constant slope therefore indicates constant speed. Hence, the distance time graph for uniform motion must be a straight line with constant slope.

Step-by-Step Solution:

Verification / Alternative check:

Imagine an object that travels 10 metres every second. After 1 second, it has moved 10 metres; after 2 seconds, 20 metres; after 3 seconds, 30 metres, and so on. Plotting these points (t, s) as (1, 10), (2, 20), (3, 30) gives a set of points that lie on a single straight line. This confirms that constant speed produces a straight line on a distance time graph. Any curvature or changing slope would indicate changing speed (acceleration or deceleration).

Why Other Options Are Wrong:

Option A (single dot at a point): A single dot would mean only one measurement, not continuous motion over time.

Option B (circle): Circles do not represent a simple functional relationship between distance and time and are not used for distance time plots.

Option D (curve that bends): A curved graph indicates that the speed is changing, meaning acceleration or deceleration, not constant speed.

Option E (zigzag broken line): A zigzag would mean abrupt changes in distance in very short times, which is not the smooth uniform motion described here.

Common Pitfalls:

Students sometimes confuse distance time graphs with velocity time graphs. For velocity time graphs, constant velocity is shown by a horizontal line. For distance time graphs, constant speed is shown by a straight line with constant, non zero slope. Remember that the type of graph and what each axis represents makes a big difference to the interpretation of the lines and shapes you see.

Final Answer:

The distance time graph is a straight line with constant slope.