State all three equations of motion. Give significance of each term used.
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State all three equations of motion. Give significance of each term used.
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Answer:
The three equations of motion describe the relationships between an object's initial velocity, final velocity, acceleration, time, and displacement. These equations are fundamental in classical mechanics. Here are the three equations of motion:
1. First Equation of Motion:
\[v = u + at\]
- \(v\) is the final velocity of the object.
- \(u\) is the initial velocity of the object.
- \(a\) is the acceleration of the object.
- \(t\) is the time taken.
2. Second Equation of Motion:
\[s = ut + \frac{1}{2}at^2\]
- \(s\) is the displacement of the object.
- \(u\) is the initial velocity of the object.
- \(a\) is the acceleration of the object.
- \(t\) is the time taken.
3. Third Equation of Motion:
\[v^2 = u^2 + 2as\]
- \(v\) is the final velocity of the object.
- \(u\) is the initial velocity of the object.
- \(a\) is the acceleration of the object.
- \(s\) is the displacement of the object.
The significance of these terms can be summarized as follows:
- Initial velocity (\(u\)) is the object's velocity at the beginning of the motion.
- Final velocity (\(v\)) is the object's velocity at the end of the motion.
- Acceleration (\(a\)) is the rate of change of velocity. It can be positive (acceleration) or negative (deceleration).
- Time (\(t\)) is the duration of the motion.
- Displacement (\(s\)) is the change in position of the object from the initial to the final point.
These equations are used to solve a wide range of problems involving the motion of objects under the influence of constant acceleration. They are fundamental in physics and engineering for analyzing and predicting the behavior of moving objects.