What are all the formulas related to acceleration, velocity, and motion?

Acceleration can be calculated using several core kinematic formulas, each suited to different data sets. The most fundamental is a = (v - u) / t, where acceleration equals the change in velocity divided by time. When you know initial velocity (u), final velocity (v), and displacement (s) but not time, use a = (v² - u²) / 2s. For motion starting from rest with known distance and time, the relationship s = ½at² can be rearranged to a = 2s / t².

These formulas interconnect through the five kinematic equations that govern uniformly accelerated motion. Beyond the basic formulas, you'll also encounter v = u + at (final velocity), s = ut + ½at² (displacement with initial velocity), and v² = u² + 2as (velocity-displacement relationship). Each equation requires three known variables to solve for a fourth, making them versatile tools for different problem types.

In practice, selecting the right formula depends on what information you have available. If a car accelerates from 20 m/s to 35 m/s over 5 seconds, use a = Δv/t = (35-20)/5 = 3 m/s². If a cyclist covers 100 meters while accelerating from rest in 10 seconds, apply a = 2s/t² = 2(100)/10² = 2 m/s². The key is matching your known variables to the appropriate equation rather than forcing one formula for every situation.