Define acceleration as change in velocity per unit time; recall and use the equation a = Δv / Δt

What is Acceleration?

Acceleration is the rate at which an object’s velocity changes over time. Think of it as the “speed‑up” or “slow‑down” of a moving object. 🚗

Mathematically, it’s expressed as the change in velocity divided by the change in time:

$a = \dfrac{\Delta v}{\Delta t}$

Analogy: The Car on the Highway

Imagine driving a car. If you press the gas pedal, the car’s speed (velocity) increases. The faster the speed increases, the higher the acceleration. If you hit the brake, the velocity decreases – that’s a negative acceleration (deceleration). 🏎️

Another example: an elevator starting from rest. The instant it begins to move, its velocity changes from 0 to a certain value, giving it a brief acceleration. 🛗

Calculating Acceleration – Step by Step

1. Identify the initial velocity ($v_i$) and final velocity ($v_f$). 📏
2. Determine the time interval ($\Delta t$) over which the change occurs. ⏱️
3. Compute the change in velocity: $\Delta v = v_f - v_i$. 🧮
4. Divide by the time interval: $a = \dfrac{\Delta v}{\Delta t}$. ??

Example Problem

Here, $\Delta v = 20 - 0 = 20$ m/s and $\Delta t = 4$ s, so $a = 20/4 = 5$ m/s². 🚀

Exam Tips for Acceleration Questions

• Always write the formula $a = \dfrac{\Delta v}{\Delta t}$ before plugging in numbers.
• Check units: velocity in m/s, time in s, so acceleration will be m/s².
• Remember that a negative $\Delta v$ or $\Delta t$ indicates deceleration.
• When given a graph, read the slope of the velocity–time curve to find acceleration.
• Practice converting between different units (e.g., km/h to m/s) to avoid mistakes.