The first equation of motion gives the relation between _________.
Velocity and time
Understanding the First Equation of Motion
The equations of motion are a set of mathematical formulas that describe the relationship between displacement, velocity, acceleration, and time for an object moving with constant acceleration. There are typically three main equations of motion.
Let's examine the first equation of motion.
The First Equation of Motion: Velocity and Time Relation
The first equation of motion is given by:
$$v = u + at$$
Where:
- $v$ is the final velocity of the object.
- $u$ is the initial velocity of the object.
- $a$ is the uniform acceleration of the object.
- $t$ is the time taken.
This equation tells us that the final velocity ($v$) of an object after a certain time ($t$) is equal to its initial velocity ($u$) plus the change in velocity ($at$) due to constant acceleration ($a$).
Looking at the equation $v = u + at$, we can clearly see that it directly relates the final velocity ($v$) and the time taken ($t$). Given the initial velocity ($u$) and constant acceleration ($a$), we can find the velocity of the object at any given time ($t$).
Let's consider the given options:
- Position and time: This relation is described by the second and third equations of motion ($s = ut + \frac{1}{2}at^2$ and $v^2 = u^2 + 2as$, where $s$ is displacement/position). The first equation does not directly give position.
- Position and velocity: While position and velocity are related in other equations, the first equation specifically connects velocity to time, not position.
- Velocity and time: As shown by the equation $v = u + at$, the first equation directly relates the final velocity ($v$) to the time ($t$) elapsed, along with initial velocity and acceleration. This is the primary relationship it describes.
- Velocity and acceleration: While acceleration ($a$) is present in the equation, the equation's main purpose is to find the velocity ($v$) at a specific time ($t$), given the acceleration. It establishes the relationship between velocity and time under constant acceleration.
Therefore, the first equation of motion most directly gives the relation between velocity and time.
Revision Table: Equations of Motion
| Equation | Relation between | Conditions for use |
|---|---|---|
| $v = u + at$ | Velocity, Time, Initial velocity, Acceleration | When final velocity or time needs to be found, and displacement ($s$) is not directly involved. |
| $s = ut + \frac{1}{2}at^2$ | Displacement, Time, Initial velocity, Acceleration | When displacement or time needs to be found, and final velocity ($v$) is not directly involved. |
| $v^2 = u^2 + 2as$ | Final velocity, Initial velocity, Acceleration, Displacement | When final velocity or displacement needs to be found, and time ($t$) is not directly involved. |
Additional Information on Equations of Motion
These equations are derived assuming that the acceleration is constant and the motion is along a straight line (one-dimensional motion). They are often referred to as the kinematic equations for uniform acceleration.
- The first equation, $v = u + at$, can be derived directly from the definition of average acceleration ($a = \frac{v-u}{t}$). Rearranging this gives $v = u + at$.
- These equations form the foundation for solving many problems involving motion with constant acceleration in physics.
- Understanding the relationship between the variables in each equation is crucial for choosing the correct equation to solve a specific problem.
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Important Questions from Motion
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