A Car Moves In One Highways At 54 Km/h At A Certain Moment The Driver Accelerates After 5s. The Car Reaches A Speed Of 90 K/h It Was Assumed That The Acceleration Was Constant The 5 S. Sketch The Speed Diagram For The Interval Of
Introduction
When a car accelerates from a standstill or from a certain speed, it undergoes a significant change in its velocity. In this article, we will explore the physics behind a car's acceleration on a highway, using a specific scenario as an example. We will analyze the car's speed over a 5-second interval, assuming a constant acceleration, and sketch the speed diagram for this interval.
The Scenario
Let's consider a car moving at a constant speed of 54 km/h on a highway. At a certain moment, the driver accelerates the car, and after 5 seconds, the car reaches a speed of 90 km/h. We will assume that the acceleration is constant over this 5-second interval.
Calculating the Acceleration
To calculate the acceleration of the car, we need to use the following formula:
a = Δv / Δt
where a is the acceleration, Δv is the change in velocity, and Δt is the time over which the acceleration occurs.
First, we need to convert the speeds from km/h to m/s:
54 km/h = 54,000 m / 3600 s = 15 m/s 90 km/h = 90,000 m / 3600 s = 25 m/s
Now, we can calculate the change in velocity:
Δv = 25 m/s - 15 m/s = 10 m/s
The time over which the acceleration occurs is 5 seconds. Therefore, we can calculate the acceleration as follows:
a = Δv / Δt = 10 m/s / 5 s = 2 m/s^2
Sketching the Speed Diagram
To sketch the speed diagram for the interval, we need to consider the following:
- The initial speed of the car is 54 km/h (15 m/s).
- The final speed of the car is 90 km/h (25 m/s).
- The acceleration is constant at 2 m/s^2.
Using the equation of motion, we can calculate the speed of the car at any given time t:
v(t) = v0 + at
where v0 is the initial speed, a is the acceleration, and t is the time.
We can plug in the values we know to get:
v(t) = 15 m/s + 2 m/s^2 * t
Now, we can sketch the speed diagram for the interval. The speed diagram will show the car's speed increasing from 15 m/s to 25 m/s over the 5-second interval.
The Speed Diagram
Here is the speed diagram for the interval:
| Time (s) | Speed (m/s) |
|---|---|
| 0 | 15 |
| 1 | 17 |
| 2 | 19 |
| 3 | 21 |
| 4 | 23 |
| 5 | 25 |
Discussion
The speed diagram shows that the car's speed increases linearly over the 5-second interval, with a constant acceleration of 2 m/s^2. This is consistent with our assumption of constant acceleration.
Conclusion
In this article, we have explored the physics behind a car's acceleration on a highway, using a specific scenario as an example. We have calculated the acceleration of the car and sketched the speed diagram for the interval. The speed diagram shows that the car's speed increases linearly over the 5-second interval, with a constant acceleration of 2 m/s^2.
Key Takeaways
- The acceleration of the car is constant at 2 m/s^2.
- The speed of the car increases linearly over the 5-second interval.
- The speed diagram shows the car's speed increasing from 15 m/s to 25 m/s over the 5-second interval.
Further Reading
If you are interested in learning more about the physics of motion, we recommend checking out the following resources:
References
- [Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. John Wiley & Sons.]
- [Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.]
A Car's Acceleration on a Highway: Q&A =============================================
Introduction
In our previous article, we explored the physics behind a car's acceleration on a highway, using a specific scenario as an example. We calculated the acceleration of the car and sketched the speed diagram for the interval. In this article, we will answer some frequently asked questions related to the topic.
Q&A
Q: What is acceleration?
A: Acceleration is the rate of change of velocity of an object with respect to time. It is a measure of how quickly an object's speed or direction changes.
Q: How is acceleration calculated?
A: Acceleration is calculated using the following formula:
a = Δv / Δt
where a is the acceleration, Δv is the change in velocity, and Δt is the time over which the acceleration occurs.
Q: What is the difference between speed and velocity?
A: Speed is a scalar quantity that refers to the rate of change of an object's position with respect to time. Velocity, on the other hand, is a vector quantity that includes both the speed and direction of an object's motion.
Q: Can acceleration be negative?
A: Yes, acceleration can be negative. This means that the object's speed is decreasing, or it is decelerating.
Q: What is the relationship between acceleration and force?
A: Acceleration is directly proportional to the force applied to an object, and inversely proportional to its mass. This is described by Newton's second law of motion:
F = ma
where F is the force applied, m is the mass of the object, and a is the acceleration.
Q: How does the speed diagram relate to the acceleration of the car?
A: The speed diagram shows the car's speed increasing linearly over the 5-second interval, with a constant acceleration of 2 m/s^2. This means that the car's speed is increasing at a constant rate, which is a characteristic of constant acceleration.
Q: What is the significance of the acceleration of the car?
A: The acceleration of the car is significant because it determines how quickly the car's speed changes. In this case, the car's speed increases from 15 m/s to 25 m/s over the 5-second interval, which is a relatively short time.
Q: Can the acceleration of the car be affected by external factors?
A: Yes, the acceleration of the car can be affected by external factors such as friction, air resistance, and the force of gravity. These factors can slow down the car's acceleration or even cause it to decelerate.
Conclusion
In this article, we have answered some frequently asked questions related to the physics of a car's acceleration on a highway. We have discussed the concept of acceleration, its calculation, and its relationship to speed and velocity. We have also explored the significance of the acceleration of the car and how it can be affected by external factors.
Key Takeaways
- Acceleration is the rate of change of velocity of an object with respect to time.
- Acceleration is calculated using the formula a = Δv / Δt.
- Speed and velocity are related but distinct concepts.
- Acceleration can be negative, indicating deceleration.
- The acceleration of an object is directly proportional to the force applied and inversely proportional to its mass.
- The speed diagram shows the car's speed increasing linearly over the 5-second interval, with a constant acceleration of 2 m/s^2.
Further Reading
If you are interested in learning more about the physics of motion, we recommend checking out the following resources:
References
- [Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. John Wiley & Sons.]
- [Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.]