Acceleration

Acceleration is one of the most fundamental concepts in physics and is a measure of how an object’s velocity changes over time. It is a vector quantity, meaning it has both magnitude and direction. It is calculated as the rate of change of velocity. In other words, acceleration tells us how quickly an object is speeding up, slowing down, or changing direction.

Average acceleration refers to the change in velocity over a certain time interval, while instantaneous acceleration refers to the change in velocity at a specific moment in time. It is important to understand the distinction between average and instantaneous acceleration because the former provides us with a general idea of how velocity is changing, while the latter gives us a precise picture of what is happening at a specific moment in time.

Formulas for each are given as:

\vec{a}_{average} = \dfrac{\Delta \vec{v}}{\Delta t} = \dfrac{\vec{v}_f - \vec{v}_i}{t_f - t_i}

\vec{a}_{instantaneous} = \displaystyle\lim_{\Delta t \to 0}\dfrac{\Delta \vec{v}}{\Delta t} = \dfrac{d \vec{v}}{dt}

Just because an object is moving fast, that doesn’t mean it is accelerating. A plane might be flying at a speed of 500 miles per hour. However, if that speed is constant, then the acceleration of the plane (at that moment) is zero. Elevators are a common example of what acceleration feels like.

Elevators are a great example of what acceleration feels like.
Elevators are a great example of what acceleration feels like.

When you are standing on the ground floor and the elevator starts moving upward, you feel an acceleration that pushes you into the floor (the same direction that gravity is pulling you). For a moment, you feel heavier. As the elevator nears the top floor, it starts to slow down (opposite the direction of gravity). For a moment, you feel lighter because the acceleration of the elevator is partially counteracting the acceleration due to gravity.

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