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Sagot :
4.1 Velocity Diagram for Speeding Up:
First, let's visualize the motion of the car as it speeds up.
```
Initial Velocity (V_i1): 20 m/s (East)
Final Velocity (V_f1): 35 m/s (East)
Time Interval (t1): 5 s
```
To draw the velocity diagram:
- Start with a horizontal arrow pointing to the right (eastward) labeled "20 m/s".
- Next to it, draw another horizontal arrow pointing to the right but longer than the first one to indicate "35 m/s".
- The difference between the two velocities (increase in velocity) is represented by a third arrow pointing to the right, which shows the direction of the acceleration.
```
20 m/s Increase in Velocity (15 m/s)
|--------------------->|------------------------------>|
Initial Velocity Final Velocity
Acceleration Arrow pointing to the right (east)
```
4.2 Calculation of Average Acceleration (Speeding Up):
To calculate the magnitude of the car's average acceleration, we use the formula:
[tex]\[ \text{Acceleration} (a) = \frac{\text{Final Velocity} (V_f) - \text{Initial Velocity} (V_i)}{\text{Time} (t)} \][/tex]
Using the given values,
[tex]\[ V_i1 = 20 \, \text{m/s}, \quad V_f1 = 35 \, \text{m/s}, \quad t1 = 5 \, \text{s} \][/tex]
[tex]\[ a1 = \frac{35 \, \text{m/s} - 20 \, \text{m/s}}{5 \, \text{s}} \][/tex]
[tex]\[ a1 = \frac{15 \, \text{m/s}}{5 \, \text{s}} \][/tex]
[tex]\[ a1 = 3.0 \, \text{m/s}^2 \][/tex]
So, the magnitude of the car's average acceleration is [tex]\(3.0 \, \text{m/s}^2\)[/tex] directed eastward.
5.1 Velocity Diagram for Slowing Down:
Next, visualize the motion of the car as it slows down.
```
Initial Velocity (V_i2): 35 m/s (East)
Final Velocity (V_f2): 25 m/s (East)
Time Interval (t2): 4 s
```
To draw the velocity diagram:
- Start with a horizontal arrow pointing to the right (eastward) labeled "35 m/s".
- Next to it, draw another horizontal arrow pointing to the right but shorter than the first one to indicate "25 m/s".
- The difference between the two velocities (decrease in velocity) is represented by a third arrow pointing to the left, showing the direction of the acceleration.
```
35 m/s Decrease in Velocity (10 m/s)
|-------------------------------->|----------------->|
Initial Velocity Final Velocity
Acceleration Arrow pointing to the left (west)
```
5.2 Calculation of Average Acceleration (Slowing Down):
Using the formula for acceleration:
[tex]\[ a = \frac{V_f - V_i}{t} \][/tex]
Using the given values,
[tex]\[ V_i2 = 35 \, \text{m/s}, \quad V_f2 = 25 \, \text{m/s}, \quad t2 = 4 \, \text{s} \][/tex]
[tex]\[ a2 = \frac{25 \, \text{m/s} - 35 \, \text{m/s}}{4 \, \text{s}} \][/tex]
[tex]\[ a2 = \frac{-10 \, \text{m/s}}{4 \, \text{s}} \][/tex]
[tex]\[ a2 = -2.5 \, \text{m/s}^2 \][/tex]
So, the magnitude of the car's acceleration is [tex]\(2.5 \, \text{m/s}^2\)[/tex] directed westward (since the acceleration is negative when east is positive).
5.3 Acceleration with West as Positive Direction:
If we take west as the positive direction, a negative acceleration (deceleration) when moving east would now be a positive acceleration (as westward is positive).
[tex]\[ a2_{\text{west positive}} = -(-2.5 \, \text{m/s}^2) = 2.5 \, \text{m/s}^2 \][/tex]
So, with west as the positive direction, the magnitude of the car's acceleration remains [tex]\(2.5 \, \text{m/s}^2\)[/tex], but it is now positive.
First, let's visualize the motion of the car as it speeds up.
```
Initial Velocity (V_i1): 20 m/s (East)
Final Velocity (V_f1): 35 m/s (East)
Time Interval (t1): 5 s
```
To draw the velocity diagram:
- Start with a horizontal arrow pointing to the right (eastward) labeled "20 m/s".
- Next to it, draw another horizontal arrow pointing to the right but longer than the first one to indicate "35 m/s".
- The difference between the two velocities (increase in velocity) is represented by a third arrow pointing to the right, which shows the direction of the acceleration.
```
20 m/s Increase in Velocity (15 m/s)
|--------------------->|------------------------------>|
Initial Velocity Final Velocity
Acceleration Arrow pointing to the right (east)
```
4.2 Calculation of Average Acceleration (Speeding Up):
To calculate the magnitude of the car's average acceleration, we use the formula:
[tex]\[ \text{Acceleration} (a) = \frac{\text{Final Velocity} (V_f) - \text{Initial Velocity} (V_i)}{\text{Time} (t)} \][/tex]
Using the given values,
[tex]\[ V_i1 = 20 \, \text{m/s}, \quad V_f1 = 35 \, \text{m/s}, \quad t1 = 5 \, \text{s} \][/tex]
[tex]\[ a1 = \frac{35 \, \text{m/s} - 20 \, \text{m/s}}{5 \, \text{s}} \][/tex]
[tex]\[ a1 = \frac{15 \, \text{m/s}}{5 \, \text{s}} \][/tex]
[tex]\[ a1 = 3.0 \, \text{m/s}^2 \][/tex]
So, the magnitude of the car's average acceleration is [tex]\(3.0 \, \text{m/s}^2\)[/tex] directed eastward.
5.1 Velocity Diagram for Slowing Down:
Next, visualize the motion of the car as it slows down.
```
Initial Velocity (V_i2): 35 m/s (East)
Final Velocity (V_f2): 25 m/s (East)
Time Interval (t2): 4 s
```
To draw the velocity diagram:
- Start with a horizontal arrow pointing to the right (eastward) labeled "35 m/s".
- Next to it, draw another horizontal arrow pointing to the right but shorter than the first one to indicate "25 m/s".
- The difference between the two velocities (decrease in velocity) is represented by a third arrow pointing to the left, showing the direction of the acceleration.
```
35 m/s Decrease in Velocity (10 m/s)
|-------------------------------->|----------------->|
Initial Velocity Final Velocity
Acceleration Arrow pointing to the left (west)
```
5.2 Calculation of Average Acceleration (Slowing Down):
Using the formula for acceleration:
[tex]\[ a = \frac{V_f - V_i}{t} \][/tex]
Using the given values,
[tex]\[ V_i2 = 35 \, \text{m/s}, \quad V_f2 = 25 \, \text{m/s}, \quad t2 = 4 \, \text{s} \][/tex]
[tex]\[ a2 = \frac{25 \, \text{m/s} - 35 \, \text{m/s}}{4 \, \text{s}} \][/tex]
[tex]\[ a2 = \frac{-10 \, \text{m/s}}{4 \, \text{s}} \][/tex]
[tex]\[ a2 = -2.5 \, \text{m/s}^2 \][/tex]
So, the magnitude of the car's acceleration is [tex]\(2.5 \, \text{m/s}^2\)[/tex] directed westward (since the acceleration is negative when east is positive).
5.3 Acceleration with West as Positive Direction:
If we take west as the positive direction, a negative acceleration (deceleration) when moving east would now be a positive acceleration (as westward is positive).
[tex]\[ a2_{\text{west positive}} = -(-2.5 \, \text{m/s}^2) = 2.5 \, \text{m/s}^2 \][/tex]
So, with west as the positive direction, the magnitude of the car's acceleration remains [tex]\(2.5 \, \text{m/s}^2\)[/tex], but it is now positive.
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