2.4 Acceleration

Key Concept

Acceleration

The measure of change in velocity with the passage of time.

a = Δv / Δt

  • Vector quantity
  • SI unit: meter per second squared (m/s²)
  • Same direction as the change in velocity
  • Can be positive (increasing velocity) or negative (decreasing velocity)
  • Can occur due to change in speed, direction, or both

Types of Acceleration

Uniform Acceleration

Velocity changes at the same rate each second. Equal changes in velocity occur in equal intervals of time.

Non-uniform Acceleration

The rate of velocity change is not steady over time. Common in real-life scenarios with varying forces.

Example Problem

Acceleration of Cheetah

Problem: A cheetah accelerates from 0 to 26.8 m/s in 3 seconds. Calculate its acceleration.

Solution:


                Given:
                Initial velocity v₁ = 0 m/s (East)
                Final velocity v₂ = 26.8 m/s (East)
                Time taken Δt = 3 s

                Using a = (v₂ - v₁) / Δt
                a = (26.8 m/s - 0 m/s) / 3 s
                a = 8.93 m/s²

The cheetah'sacceleration is 8.93 m/s² towards the East.

Visual Concept Check

Can You Tell?

Identify the acceleration in each case:

  • v₁ = 2 m/s, v₂ = 2 m/s
  • v₁ = 2 m/s, v₂ = 4 m/s
  • v₁ = 3 m/s, v₂ = 1 m/s
  • v₁ = 2 m/s, v₂ = 1 m/s
  • v₁ = 3 m/s, v₂ = 4 m/s

Historical Note

Galileo's Contribution: First scientist to measure speed as distance over time. He discovered that objects of different masses fall at the same rate, introducing the concept of gravitational acceleration (g).