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.
Answers
GPT-4o mini
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.
### 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.