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

1.2 Motion

Objective

Define acceleration as change in velocity per unit time; recall and use the equation \$a = \frac{\Delta v}{\Delta t}\$.

Key Concepts

• Velocity is a vector quantity describing speed and direction.
• Acceleration is the rate of change of velocity.
• Units of acceleration: m/s².

Definition of Acceleration

Acceleration is the change in velocity of an object per unit time:

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

Interpreting the Equation

1. Calculate the difference in velocity: \$\Delta v = v{\text{final}} - v{\text{initial}}\$.
2. Determine the time interval over which the change occurs: \$\Delta t\$.
3. Divide \$\Delta v\$ by \$\Delta t\$ to obtain acceleration.

Example Problem

Car A accelerates from rest to 20 m/s in 5 s. Find its acceleration.

1. \$\Delta v = 20\,\text{m/s} - 0\,\text{m/s} = 20\,\text{m/s}\$
2. \$\Delta t = 5\,\text{s}\$
3. \$a = \frac{20\,\text{m/s}}{5\,\text{s}} = 4\,\text{m/s}^2\$

Units Table

Quantity	Symbol	Units
Velocity	\$v\$	m/s
Change in velocity	\$\Delta v\$	m/s
Time interval	\$\Delta t\$	s
Acceleration	\$a\$	m/s²