Distance covered by object is ______ to time.
directly proportional
Understanding the Relationship Between Distance and Time
The question asks about the relationship between the distance covered by an object and the time taken to cover that distance. This is a fundamental concept in physics, specifically in the study of motion.
Let's consider an object moving at a constant speed. Speed is defined as the distance covered per unit time. The formula for speed is:
\( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \)
We can rearrange this formula to express distance in terms of speed and time:
\( \text{Distance} = \text{Speed} \times \text{Time} \)
Using symbols, if \(d\) is the distance, \(v\) is the speed, and \(t\) is the time, the formula is:
\( d = v \times t \)
Analyzing Proportionality
The question asks about the proportionality between distance and time. Proportionality describes how one quantity changes in relation to another.
- Direct Proportionality: Two quantities are directly proportional if an increase in one quantity causes a proportional increase in the other, and a decrease causes a proportional decrease. Mathematically, if \(y\) is directly proportional to \(x\), we write \(y \propto x\), which means \(y = kx\) for some constant \(k\).
- Inversely Proportionality: Two quantities are inversely proportional if an increase in one quantity causes a proportional decrease in the other. Mathematically, if \(y\) is inversely proportional to \(x\), we write \(y \propto \frac{1}{x}\), which means \(y = \frac{k}{x}\) for some constant \(k\).
Distance and Time Relationship at Constant Speed
Looking at the formula \(d = v \times t\), if the speed \(v\) is constant, then \(v\) acts like the constant of proportionality (\(k\)) in the direct proportionality equation \(y = kx\). In this case, distance (\(d\)) corresponds to \(y\), time (\(t\)) corresponds to \(x\), and speed (\(v\)) corresponds to \(k\).
So, when the speed of an object is constant, the distance covered is directly proportional to the time taken. This means:
- If you double the time, you double the distance.
- If you triple the time, you triple the distance.
- If you halve the time, you halve the distance.
This relationship holds true for motion at a constant speed.
Evaluating the Options
- equal proportional: This is not a standard term for proportionality. Distance is not necessarily "equal" to time; it depends on the speed.
- directly proportional: As explained above, when speed is constant, distance is directly proportional to time.
- inversely proportional: This would mean that as time increases, distance decreases, which is incorrect for an object moving forward.
- double proportional: This is not a standard term for proportionality. It might imply a relationship like \(d \propto t^2\) or \(d \propto 2t\), but the basic relationship at constant speed is \(d \propto t\).
Therefore, the correct description of the relationship between distance covered and time, assuming constant speed, is directly proportional.
| Term | Meaning | Mathematical Relation (k is constant) | Distance-Time Relation (at constant speed v) |
|---|---|---|---|
| Directly Proportional | As one increases, the other increases proportionally. | \(y \propto x \implies y = kx\) | \(d \propto t \implies d = vt\) |
| Inversely Proportional | As one increases, the other decreases proportionally. | \(y \propto \frac{1}{x} \implies y = \frac{k}{x}\) | Not applicable for distance vs. time at constant speed. |
Revision Table: Key Motion Concepts
| Concept | Definition | Formula (at constant speed) |
|---|---|---|
| Distance | Total length of the path covered by an object. | \(d = v \times t\) |
| Time | Duration for which the motion occurs. | \(t = \frac{d}{v}\) |
| Speed | Distance covered per unit time. | \(v = \frac{d}{t}\) |
| Direct Proportionality | Relationship where one quantity changes directly with another (\(y = kx\)). | \(d \propto t\) (if \(v\) is constant) |
Additional Information on Distance, Time, and Motion
While the direct proportionality between distance and time is clear for motion at constant speed, it's important to remember that speed isn't always constant.
- Motion with Acceleration: When an object is accelerating (speed is changing), the relationship between distance and time is more complex. For uniform acceleration starting from rest, the distance covered is proportional to the square of the time (\(d \propto t^2\)). The formula involves initial velocity, acceleration, and time: \(d = ut + \frac{1}{2}at^2\), where \(u\) is initial velocity and \(a\) is acceleration.
- Instantaneous vs. Average Speed: The speed we discussed (\(v = d/t\)) is often the average speed over the time interval. Instantaneous speed is the speed at a particular moment.
- Velocity: Velocity is speed with direction. It is a vector quantity, whereas distance and speed are scalar quantities.
Understanding the basic direct proportionality in the case of constant speed is foundational before exploring more complex scenarios involving changing speed or direction.
Important Questions from Laws and Principles
TV remote controls work on the principle of ________.
Which of the following laws deduces the expression for the force between two stationary point charges in vacuum or free space?
Name the law in Physics which states that equal volume of all gases under the same conditions of temperature and pressure contain the equal number of molecules.
What do you call the effect of splitting of a spectral line into several components in the presence of a static magnetic field?
According to _____, pressure is equal to the force divided by the area on which it acts.
