Question

A brick falls freely from a building and hits the ground after 5s. Please draw the distance – time, speed – time and acceleration – time graphs of this motion.

Answer 1

To analyze the motion of a brick falling freely from a building, we'll break it down into three graphs: distance-time, speed-time, and acceleration-time.

### 1. Distance-Time Graph
In free fall, the distance fallen (d) over time (t) can be described by the equation of motion:

\[ d = \frac{1}{2} g t^2 \]

where \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)). Since the brick falls for 5 seconds, you can calculate the distance fallen at \( t = 5 \, \text{s} \):

\[ d = \frac{1}{2} \times 9.81 \, \text{m/s}^2 \times (5 \, \text{s})^2 = \frac{1}{2} \times 9.81 \times 25 = 122.625 \, \text{m} \]

The graph will be a parabola opening upwards; it starts at the origin and increases as time goes on, showing that distance increases with the square of time.

### 2. Speed-Time Graph
The speed (v) of the brick can be calculated using the equation:

\[ v = g t \]

At \( t = 0 \, \text{s} \), \( v = 0 \, \text{m/s} \), and at \( t = 5 \, \text{s} \):

\[ v = 9.81 \, \text{m/s}^2 \times 5 \, \text{s} = 49.05 \, \text{m/s} \]

The graph is a straight line starting from the origin (0,0) and rising linearly to the point (5, 49.05). The slope of the line is constant, reflecting the constant acceleration due to gravity.

### 3. Acceleration-Time Graph
In free fall, the acceleration (a) is constant and equal to \( g \):

\[ a = 9.81 \, \text{m/s}^2 \]

This means the acceleration-time graph will be a horizontal line at \( y = 9.81 \, \text{m/s}^2 \) for the entire time of the fall (0 to 5 seconds).

---

### Representation of the Graphs

**Distance-Time Graph**
```
Distance (m)
|
| *
| *
| *
| *
| *
| *
| *
|__________________________
Time (s)
```

**Speed-Time Graph**
```
Speed (m/s)
|
| *
| *
| *
| *
| *
| *
| *
|__________________________
Time (s)
```

**Acceleration-Time Graph**
```
Acceleration (m/s²)
|
|-------------------------------------------
| g = 9.81
|-------------------------------------------
|__________________________
Time (s)
```

These graphs illustrate the physics of free fall: distance increases quadratically with time, speed increases linearly, and acceleration remains constant.