Speed, velocity and acceleration — KCSE Physics

In physics, kinematic equations describe the motion of objects under uniform acceleration. The three main equations are:

1. v = u + at

   • Where:
     • v = final velocity
     • u = initial velocity
     • a = acceleration
     • t = time

2. s = ut + ½at²

   • Where:
     • s = displacement

3. v² = u² + 2as

   • This relates final and initial velocities to displacement and acceleration.

To apply these equations, identify known and unknown variables, then choose the appropriate equation. For instance, if an object starts from rest (u = 0), accelerates at 2 m/s² for 5 seconds, you can find:

• Final velocity (v):

  • Using v = u + at:
  • v = 0 + (2 m/s² * 5 s)
  • v = 10 m/s

• Displacement (s):

  • Using s = ut + ½at²:
  • s = 0 * 5 + ½ * 2 * (5)²
  • s = 0 + 25 = 25 m

Practice these equations to solve different problems effectively.

Velocity-time graphs provide a visual representation of an object's motion. The slope of the graph indicates acceleration, while the area under the graph represents distance travelled.

Key concepts:

• Slope: The steepness of the line indicates acceleration. A steeper slope means greater acceleration.
• Positive slope: Indicates positive acceleration (speeding up).
• Negative slope: Indicates negative acceleration (slowing down).
• Horizontal line: Indicates constant velocity (no acceleration).
• Area under the graph: Represents the total distance travelled during the time interval.

To calculate acceleration, use the formula:
Acceleration (a) = Change in velocity (Δv) / Time (Δt).
To find the distance from the area under the graph, calculate the area of shapes formed (triangles, rectangles).

Ticker-tape analysis is essential for understanding motion. A ticker-tape recorder marks dots at regular time intervals. By analyzing the spacing of these dots, we can determine both velocity and acceleration.

Velocity is calculated using the formula:
[ \text{Velocity} = \frac{\text{Distance}}{\text{Time}} ]
To find the distance, measure the length between two dots and the time is the interval between them.

Acceleration is the change in velocity over time, given by:
[ \text{Acceleration} = \frac{\text{Change in Velocity}}{\text{Time}} ]
A ticker-tape with evenly spaced dots indicates constant velocity, while varying distances between dots indicate acceleration.

For example, if the distance between dots increases, the object is accelerating. Conversely, if the dots are evenly spaced, the object moves at a constant velocity.