Calculating Uniform Acceleration

Definition of Uniform Acceleration

Acceleration is the rate of change of velocity. Uniform acceleration means acceleration that is constant over time. This means the velocity of an object changes by the same amount every second.

If an object speeds up or slows down steadily, it has uniform acceleration.

This differs from non-uniform acceleration, where the rate of change of velocity varies at different times (e.g., a car slowing down unevenly in traffic). The equations for uniform acceleration do not apply in cases of non-uniform acceleration.

Key Equations for Uniform Acceleration

There are three main equations used to calculate motion with uniform acceleration. These relate initial velocity, final velocity, acceleration, time, and displacement:

• Final velocity: $v = u + at$
• Displacement: $s = ut + \frac{1}{2}at^2$
• Velocity squared: $v^2 = u^2 + 2as$

Symbols:

• $u$ = initial velocity (m/s)
• $v$ = final velocity (m/s)
• $a$ = acceleration (m/s²)
• $t$ = time (s)
• $s$ = displacement (m)

These equations only apply when acceleration is constant (uniform acceleration).

Calculating Acceleration

Acceleration can be calculated from velocity and time data using the formula:

$$a = \frac{v - u}{t}$$

This means acceleration is the change in velocity divided by the time taken for that change.

The unit of acceleration is metres per second squared ($\text{m/s}^2$).

For example, if a cyclist increases speed from 5 m/s to 15 m/s in 4 seconds, the acceleration is:

$$a = \frac{15 - 5}{4} = \frac{10}{4} = 2.5 \text{ m/s}^2$$

Solving Problems Involving Uniform Acceleration

When solving problems with uniform acceleration, follow these steps:

• Identify the known quantities (e.g., $u$, $v$, $a$, $t$, $s$) and the unknown you need to find.
• Choose the correct equation that includes the knowns and the unknown.
• Rearrange the equation algebraically to isolate the unknown variable.
• Substitute the values with correct units and calculate the answer.
• Check your units and whether the answer makes sense physically.

For example, if a car accelerates uniformly from 0 m/s to 20 m/s over 8 seconds, the acceleration is:

$$a = \frac{v - u}{t} = \frac{20 - 0}{8} = 2.5 \text{ m/s}^2$$