______ time graph shows speed of an object.
Distance
Understanding Speed and Motion Graphs
The question asks which type of time graph shows the speed of an object. To answer this, we need to understand what speed is and how different types of motion graphs represent physical quantities like distance, displacement, velocity, acceleration, and time.
What is Speed?
Speed is defined as the rate at which an object covers distance. Mathematically, speed is calculated as:
$$ \text{Speed} = \frac{\text{Distance travelled}}{\text{Time taken}} $$
It is a scalar quantity, meaning it only has magnitude and no direction.
Types of Motion Graphs and What They Show
Different graphs plot different quantities against time to represent the motion of an object. The slope of these graphs provides information about other related quantities.
- Distance-Time Graph: This graph plots the total distance covered by an object against time. The slope of a distance-time graph at any point gives the speed of the object at that instant. A straight line on a distance-time graph indicates uniform speed, while a curved line indicates non-uniform speed.
- Displacement-Time Graph: This graph plots the displacement of an object from a reference point against time. Displacement is a vector quantity (it has both magnitude and direction). The slope of a displacement-time graph gives the velocity of the object.
- Velocity-Time Graph: This graph plots the velocity of an object against time. Velocity is also a vector quantity. The slope of a velocity-time graph gives the acceleration of the object. The area under the velocity-time graph gives the displacement of the object.
- Acceleration-Time Graph: This graph plots the acceleration of an object against time. The area under the acceleration-time graph gives the change in velocity of the object.
Analyzing the Options
Let's consider what each option's time graph shows:
- Velocity-Time Graph: As discussed, a velocity-time graph shows acceleration (from its slope) and displacement (from the area under the curve). It does NOT directly show speed for a moving object, although the magnitude of velocity is speed. However, the graph specifically plots velocity, which includes direction.
- Distance-Time Graph: This graph plots distance against time. The rate of change of distance with respect to time is speed. Therefore, a distance-time graph directly represents how speed changes over time through its slope.
- Displacement-Time Graph: A displacement-time graph shows velocity (from its slope). While the magnitude of velocity is speed, the graph itself represents displacement and velocity, not speed directly, especially in cases of non-straight-line motion where distance and displacement differ.
- Acceleration-Time Graph: An acceleration-time graph shows the change in velocity (from the area under the curve). It does not directly show speed.
Conclusion on Time Graphs and Speed
Based on the definitions and properties of motion graphs, the graph that directly shows the speed of an object through the relationship between the quantities plotted is the distance-time graph. The slope of the distance-time graph is equal to the speed.
| Graph Type | Y-axis Quantity | X-axis Quantity | Slope Represents | Area Under Curve Represents |
|---|---|---|---|---|
| Distance-Time | Distance | Time | Speed | Not commonly interpreted |
| Displacement-Time | Displacement | Time | Velocity | Not commonly interpreted |
| Velocity-Time | Velocity | Time | Acceleration | Displacement |
| Acceleration-Time | Acceleration | Time | Not commonly interpreted | Change in Velocity |
Therefore, a distance time graph shows the speed of an object.
Revision Table: Key Motion Graph Concepts
| Concept | Definition | Related Graph | Interpretation on Graph |
|---|---|---|---|
| Speed | Rate of change of distance | Distance-Time | Slope |
| Velocity | Rate of change of displacement | Displacement-Time, Velocity-Time | Slope (Displacement-Time), Y-axis value (Velocity-Time) |
| Acceleration | Rate of change of velocity | Velocity-Time, Acceleration-Time | Slope (Velocity-Time), Y-axis value (Acceleration-Time) |
| Displacement | Change in position (vector) | Displacement-Time, Velocity-Time | Y-axis value (Displacement-Time), Area under curve (Velocity-Time) |
| Distance | Total path length covered (scalar) | Distance-Time | Y-axis value |
Additional Information: Uniform vs. Non-uniform Speed
The shape of the distance-time graph tells us about the nature of the speed:
- Uniform Speed: If an object moves at a constant speed, its distance-time graph is a straight line with a positive slope. This means the object covers equal distances in equal intervals of time.
- Non-uniform Speed: If an object's speed changes, its distance-time graph is a curved line. A curve that is getting steeper indicates increasing speed, while a curve that is becoming flatter indicates decreasing speed.
Understanding these graphs is fundamental to analyzing motion in physics.
Important Questions from Motion
The motion of a particle of mass m is described by the relation, y = ut - 1⁄2 gt2, where u is the initial velocity of the particle. The force acting on the particle is
The motion of ______ body is an example of uniformly accelerated motion.
- in a particular direction is velocity.
Motion of an object is if its velocity is constant.
The motion of the body moving along a circular path is an example of ______.
