Know that a deceleration is a negative acceleration and use this in calculations

1.2 Motion – Deceleration & Negative Acceleration

1.2.1 What is Acceleration?

Acceleration is the rate at which an object's velocity changes over time. It can be positive (speeding up) or negative (slowing down). The basic definition is:

\$a = \dfrac{\Delta v}{\Delta t} = \dfrac{vf - vi}{t}\$

  • Positive acceleration → velocity increases.

  • Negative acceleration → velocity decreases.

  • Zero acceleration → constant velocity.

1.2.2 Deceleration = Negative Acceleration

When an object slows down, its acceleration is negative relative to the chosen positive direction. In other words, deceleration is simply negative acceleration.

If the velocity is decreasing, then:

\$a < 0\$

1.2.3 Everyday Example 🚗

Picture a car moving forward. When you press the brake, the car slows down. The acceleration vector points opposite to the direction of motion, so it is negative. Think of it like a skateboarder who pushes the brakes to stop – the force you apply is opposite to the direction of travel.

1.2.4 Calculating Deceleration

Use the same kinematic equations, but remember to plug in a negative value for \$a\$ when the object is slowing down.

  1. Identify the initial velocity \$vi\$, final velocity \$vf\$, time \$t\$, or distance \$s\$.

  2. Choose a positive direction (e.g., forward).

  3. Use the formula \$a = \dfrac{vf - vi}{t}\$ or \$vf^2 = vi^2 + 2 a s\$.

  4. If the object is slowing down, the calculated \$a\$ will be negative.

1.2.5 Example: Car Braking 🚘

\$v_i\$ (m/s)\$v_f\$ (m/s)\$t\$ (s)\$a\$ (m/s²)
2005\$-4\$

Calculation: \$a = \dfrac{0 - 20}{5} = -4 \text{ m/s}^2\$. The negative sign tells us the car is slowing down.

1.2.6 Practice Problems 🏁

  1. A skateboarder slows from 5 m/s to 0 m/s in 4 s. Find the deceleration.

  2. A train slows from 30 m/s to 10 m/s in 12 s. Find the deceleration.

  3. A bike travels 100 m while slowing from 15 m/s to 5 m/s. Find the deceleration.

Tip: If \$vf < vi\$, the acceleration will be negative. Plug the numbers into \$a = \dfrac{vf - vi}{t}\$ or use \$vf^2 = vi^2 + 2 a s\$ if time is not given.