Question

A car starts from rest and accelerate uniformly until it reaches a speed of 30m/s after 15s. It then maintains this speed for another 30s then the car decelerates uniformly until it is brought to rest after a further 5 seconds.
Draw the velocity time graph of the motion of the car

Answer 1

To draw the velocity-time graph for the car's motion based on the provided information, we can break down the motion into three phases:

1. **Acceleration Phase**:
- **Duration**: 15 seconds
- **Initial Velocity**: 0 m/s (starts from rest)
- **Final Velocity**: 30 m/s

Since the car accelerates uniformly from 0 m/s to 30 m/s in 15 seconds, the velocity increases linearly.

2. **Constant Velocity Phase**:
- **Duration**: 30 seconds
- **Velocity**: 30 m/s

During this phase, the velocity remains constant.

3. **Deceleration Phase**:
- **Duration**: 5 seconds
- **Initial Velocity**: 30 m/s
- **Final Velocity**: 0 m/s (comes to rest)

The car decelerates uniformly, which means the velocity decreases linearly back to 0 m/s.

### Steps to Plot:

1. **Acceleration Phase (0 to 15 seconds)**:
- A line starts at the origin (0,0) and reaches the point (15, 30) on the graph (15 seconds and 30 m/s).

2. **Constant Velocity Phase (15 to 45 seconds)**:
- From (15, 30) to (45, 30), draw a horizontal line at 30 m/s for 30 seconds.

3. **Deceleration Phase (45 to 50 seconds)**:
- From (45, 30) to (50, 0), draw a line that slopes downward from 30 m/s to 0 m/s over 5 seconds.

### Resulting Graph Description:
- The graph consists of three segments:
- An increasing linear segment from (0, 0) to (15, 30).
- A horizontal line segment from (15, 30) to (45, 30).
- A decreasing linear segment from (45, 30) to (50, 0).

### Overall Structure
- **X-axis**: Time in seconds (0 to 50 s)
- **Y-axis**: Velocity in m/s (from 0 to 30 m/s)
- The graph should have a slope for the first section, be flat in the second, and have a downward slope in the third section.

If you were to sketch this, you would end up with a triangular shape for the acceleration and deceleration phases and a rectangle for the constant velocity phase.