Lesson 9: Summary on Uniformly accelerated motion in 1D
- Acceleration :- is defined as the rate of change of velocity per unit time, and
- it can occur when there is a change in the magnitude or direction of an object’s velocity.
- Since acceleration is a vector quantity, it has both magnitude and direction, and
- its SI unit is meters per second squared (m/s²).
- It’s important to note that negative acceleration doesn’t necessarily mean deceleration;
- it depends on the signs of velocity and acceleration.
- If both velocity and acceleration have the same sign (either both positive or both negative), the object is speeding up. Conversely,
- if they have opposite signs, the object is slowing down.
- Acceleration can be positive (when velocity increases over time), negative (when velocity decreases over time, also known as retardation), or zero (when there is no change in velocity).
- Several examples illustrate acceleration in daily life, such as an apple falling from a tree, the moon orbiting the Earth, or a car accelerating from a stop at traffic lights.
- These examples demonstrate that acceleration occurs with changes in speed or direction of a moving object.
- The mathematical expression for acceleration is given by the formula:
- $accleration=\frac{\left( final velocity \right)-\left( initial velocity \right)}{time}$
- $accleration=\frac{Change in velociy}{time}$
- $\overrightarrow{a}=\frac{\Delta V}{t}$
- Average acceleration is calculated by dividing the total change in velocity by the total time taken, denoted as $\overrightarrow{a}=\frac{\Delta V}{t}=\frac{V_{f}-V_{i}}{t_{f}-t_{i}}$.
- Instantaneous acceleration is the rate at which velocity changes at a specific moment in time, and
- In uniform acceleration, where velocity changes by equal amounts in equal time intervals, the average acceleration equals the instantaneous acceleration, and
- the average velocity can be found using $V_{av}=\frac{V_{i}+V_{f}}{2}$.
- Non-uniform acceleration occurs when velocity changes by unequal amounts in equal intervals of time.