Answer :
Answer:
I'm sorry, but it seems like there's some missing information in your question, particularly regarding the units and data for the velocity-time graph. Could you please provide more details or clarify the information so I can assist you accurately?
Answer:
To calculate the acceleration from the velocity-time graph, we need to find the slope of the graph, which represents the rate of change of velocity (i.e., acceleration).
Given that the graph represents velocity in km/h and time in hours:
1. **Acceleration in the first hour:**
We need to find the change in velocity and divide it by the time interval.
- Initial velocity, \( u = 40 \) km/h
- Final velocity, \( v = 26 \) km/h
- Time interval, \( t = 1 \) hour
Using the formula for acceleration:
\[ a = \frac{v - u}{t} \]
\[ a = \frac{26 - 40}{1} \]
\[ a = \frac{-14}{1} \]
\[ a = -14 \, \text{km/h}^2 \]
The negative sign indicates that the car is decelerating.
2. **Acceleration in the last 2 hours:**
We can use the same formula, but this time, we'll consider the change in velocity and time over the last 2 hours.
- Initial velocity, \( u = 23 \) km/h
- Final velocity, \( v = 45 \) km/h
- Time interval, \( t = 2 \) hours
\[ a = \frac{v - u}{t} \]
\[ a = \frac{45 - 23}{2} \]
\[ a = \frac{22}{2} \]
\[ a = 11 \, \text{km/h}^2 \]
This positive acceleration indicates that the car is accelerating.
Now, to find the total distance travelled by the car:
- The area under the velocity-time graph represents the distance travelled.
- We can divide the graph into two sections: a trapezoid (for the first hour) and a rectangle (for the last 2 hours).
- The total distance will be the sum of the distances covered in these two sections.
For the first hour:
- Initial velocity, \( u = 40 \) km/h
- Final velocity, \( v = 26 \) km/h
- Time interval, \( t = 1 \) hour
\[ \text{Distance} = \frac{1}{2} \times (u + v) \times t \]
\[ \text{Distance} = \frac{1}{2} \times (40 + 26) \times 1 \]
\[ \text{Distance} = \frac{1}{2} \times 66 \]
\[ \text{Distance} = 33 \] km
For the last 2 hours:
- Velocity, \( v = 45 \) km/h
- Time interval, \( t = 2 \) hours
\[ \text{Distance} = v \times t \]
\[ \text{Distance} = 45 \times 2 \]
\[ \text{Distance} = 90 \] km
Total distance travelled by the car = \( 33 + 90 = 123 \) km.
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