Question

QUESTION ONE
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 construct the velocity-time graph for the car's motion based on the provided information, let's break down the motion into three phases:

1. **Acceleration Phase (0 to 15 seconds)**:
- The car starts from rest and accelerates uniformly to a speed of 30 m/s over 15 seconds.
- The velocity at the end of this phase is 30 m/s.

2. **Constant Velocity Phase (15 to 45 seconds)**:
- The car maintains a constant speed of 30 m/s for 30 seconds.
- Velocity remains at 30 m/s during this entire interval.

3. **Deceleration Phase (45 to 50 seconds)**:
- The car decelerates uniformly from 30 m/s to 0 m/s over a period of 5 seconds.
- The velocity at the end of this phase is 0 m/s.

### Simplified Phases:

1. **Acceleration (0 to 15s)**:
- From 0 m/s to 30 m/s in 15 seconds.
- This creates a straight line with a positive slope.

2. **Constant Speed (15 to 45s)**:
- From 30 m/s to 30 m/s (horizontal line) from t = 15s to t = 45s.

3. **Deceleration (45 to 50s)**:
- From 30 m/s to 0 m/s in 5 seconds.
- This creates a straight line with a negative slope.

### Constructing the Velocity-Time Graph:

- X-axis will represent time (in seconds).
- Y-axis will represent velocity (in m/s).

1. Start from the origin (0,0).
2. Draw a line from (0,0) to (15,30) for acceleration.
3. Draw a horizontal line from (15,30) to (45,30) for constant speed.
4. Draw a line from (45,30) to (50,0) for deceleration.

The resulting graph should look like this:

```
Velocity (m/s)
30 | _____________
| |
| |
| |
| _________ |
| / |
0 |__________/___________|___________________________
0 15 45 50
Time (s)
```

### Summary of Phases:
- **0 to 15s**: Linear acceleration from 0 to 30 m/s.
- **15 to 45s**: Constant velocity at 30 m/s.
- **45 to 50s**: Linear deceleration from 30 m/s to 0 m/s.

This graph accurately represents the motion sequence of the car as described in the original problem.