Table of Contents
- Velocity-Time Graph - Answers and Workings
- Question 1: Initial velocity at t=0s
- Question 2: Acceleration between 0-2 seconds
- Question 3: Motion between points P and Q
- Question 4: Distance traveled between 2-4 seconds
- Question 5: Motion between points Q and R
- Question 6: Deceleration between Q and R
- Question 7: Total distance traveled over 8 seconds
- Question 8: Duration of stationary period
- Key Concepts Demonstrated:
Velocity-Time Graph – Answers and Workings #
Question 1: Initial velocity at t=0s #
Answer: 5 m/s
Working: Reading directly from the y-axis where the line starts at t=0s
Question 2: Acceleration between 0-2 seconds #
Answer: 2.5 m/s²
Working:
- Change in velocity = 10 m/s – 5 m/s = 5 m/s
- Time taken = 2 seconds
- Acceleration = change in velocity ÷ time
- = 5 ÷ 2 = 2.5 m/s²
Question 3: Motion between points P and Q #
Answer: Constant velocity
Working:
- The line is horizontal between P and Q
- Velocity remains constant at 10 m/s
- Time period: 2s to 4s
Question 4: Distance traveled between 2-4 seconds #
Answer: 20 meters
Working:
- Area under the line between t=2s and t=4s
- Rectangle: width × height
- = 2 seconds × 10 m/s
- = 20 meters
Question 5: Motion between points Q and R #
Answer: Deceleration/negative acceleration
Working:
- Line slopes downward from Q to R
- Velocity decreases from 10 m/s to 0 m/s
Question 6: Deceleration between Q and R #
Answer: -5 m/s²
Working:
- Change in velocity = 0 m/s – 10 m/s = -10 m/s
- Time taken = 2 seconds
- Deceleration = change in velocity ÷ time
- = -10 ÷ 2 = -5 m/s²
Question 7: Total distance traveled over 8 seconds #
Answer: 45 meters
Working:
First section (0-2s):
- Trapezoid area = ½(a + b)h
- = ½(5 + 10) × 2
- = 15 meters
Second section (2-4s):
- Rectangle = 10 × 2
- = 20 meters
Third section (4-6s):
- Triangle area = ½ × base × height
- = ½ × 2 × 10
- = 10 meters
Fourth section (6-8s):
- Stationary, no distance
- = 0 meters
Total = 15 + 20 + 10 + 0 = 45 meters
Question 8: Duration of stationary period #
Answer: 2 seconds
Working:
- Object is stationary when velocity is 0 m/s
- This occurs from t=6s to t=8s
- Duration = 8 – 6 = 2 seconds
Key Concepts Demonstrated: #
- Reading velocity values directly from the graph
- Calculating acceleration from the gradient
- Finding distance by calculating area under the line
- Identifying different types of motion from line shape
- Using different area formulas (rectangle, triangle, trapezoid) for different sections
