Velocity time graph analysis, acceleration calc

🏎 1. Velocity-Time (v-t) Graphs

🔹 Axes

• Y-axis → Velocity (m/s)

• X-axis → Time (s)

🔹 Key Features

🔹 Calculating Distance

• Area under the graph = distance

• Formulas:

  • Rectangle → width × height

  • Triangle → ½ × base × height

Example:

• Triangle area: ½ × 4 s × 10 m/s = 20 m

• Rectangle area: 5 s × 8 m/s = 40 m

• Total distance = 60 m

⚡ 2. Acceleration Calculations

🔹 Definition

• Acceleration (a) = rate of change of velocity

a=change in velocitytimea = \frac{\text{change in velocity}}{\text{time}}a=timechange in velocity​

🔹 Formula

a=v−uta = \frac{v - u}{t}a=tv−u​

• vvv = final velocity (m/s)

• uuu = initial velocity (m/s)

• ttt = time (s)

🔹 Example Calculation

• Initial velocity u=2 m/su = 2\,\text{m/s}u=2m/s

• Final velocity v=10 m/sv = 10\,\text{m/s}v=10m/s

• Time t=4 st = 4\,\text{s}t=4s

a=10−24=84=2 m/s²a = \frac{10 - 2}{4} = \frac{8}{4} = 2\,\text{m/s²}a=410−2​=48​=2m/s²

🔹 Key Tips

• Positive slope → positive acceleration

• Negative slope → deceleration (negative acceleration)

• Area under graph → distance

🔗 Big Links

• V-t graphs → visual representation of motion

• Acceleration = slope of the graph

• Distance = area under the graph

⭐ Exam Tips

• Always label velocity and time axes

• Identify slope → acceleration

• Use correct units → m/s² for acceleration, m for distance

• Practice both slope and area methods