Use the formula: s = ut + ½at² → s = (28 × 3) + (½ × 2 × 3²) = 84 + (1 × 9) = <<84+9=93>>93 m - inBeat

Understanding the Context

What Does the Formula s = ut + ½at² Mean?

The expression s = ut + ½at² describes the distance s covered by an object undergoing constant acceleration (a), starting from an initial velocity (u) over a time interval (t). It combines linear velocity and acceleration effects to model motion precisely — essential for tasks ranging from vehicle dynamics to space mission planning.

• Key Terms Explained:
  
  • Initial velocity (u): The object’s speed and direction at the starting moment.
    
  • Acceleration (a): The rate of change of velocity (measured in m/s²).
    
  • Time (t): Duration for which the object moves under the influence of acceleration.
    
  • Displacement (s): The net distance from the starting point — not necessarily the path length.

Key Insights

A Step-by-Step Breakdown Using the Formula

Let’s walk through a common scenario to apply the formula effectively. Suppose a car accelerates from rest with constant acceleration over 3 seconds.

Given:

• Initial velocity, u = 28 m/s
  
• Time, t = 3 seconds
  
• Acceleration, a = 2 m/s²

Step 1: Plug values into the formula
s = ut + ½at²
s = (28 × 3) + (½ × 2 × 3²)

Final Thoughts

Step 2: Compute each term separately

• First term: 28 × 3 = 84 meters
  
• Acceleration factor: ½ × 2 = 1, then 1 × 3² = 1 × 9 = 9 meters

Step 3: Add the results
s = 84 + 9 = 93 meters

This means the car travels 93 meters in 3 seconds under constant acceleration, starting from rest with a constant 2 m/s² increase in velocity.

Why This Formula Matters in Real-World Applications

Understanding and correctly applying s = ut + ½at² is crucial across many fields: