A Car Is Traveling In A Race. The Car Went From An Initial Velocity Of $35 , \text{m/s}$ To A Final Velocity Of $65 , \text{m/s}$ In 5 Seconds. What Is The Acceleration?A. − 13 M/s 2 -13 \, \text{m/s}^2 − 13 M/s 2 B. $-6 ,
Introduction
In the world of physics, acceleration is a fundamental concept that describes the rate of change of velocity of an object. It is a measure of how quickly an object's speed or direction changes over a given period of time. In this article, we will explore the concept of acceleration using a real-world example - a car racing on a track.
What is Acceleration?
Acceleration is defined as the rate of change of velocity. It is a vector quantity, which means it has both magnitude and direction. In other words, acceleration is a measure of how quickly an object's speed or direction changes over a given period of time.
The Formula for Acceleration
The formula for acceleration is:
a = Δv / Δt
where:
- a is the acceleration
- Δv is the change in velocity (final velocity - initial velocity)
- Δt is the time over which the acceleration occurs
The Problem
A car is traveling in a race. The car went from an initial velocity of $35 , \text{m/s}$ to a final velocity of $65 , \text{m/s}$ in 5 seconds. What is the acceleration?
Solving the Problem
To solve this problem, we need to plug in the values given in the problem into the formula for acceleration.
First, we need to find the change in velocity (Δv). We can do this by subtracting the initial velocity from the final velocity:
Δv = v_f - v_i = 65 m/s - 35 m/s = 30 m/s
Next, we need to find the time over which the acceleration occurs (Δt). We are given that the time is 5 seconds.
Now, we can plug in the values into the formula for acceleration:
a = Δv / Δt = 30 m/s / 5 s = 6 m/s^2
The Answer
Therefore, the acceleration of the car is 6 m/s^2.
Discussion
The answer we obtained is positive, which means that the car is accelerating in the positive direction. This is expected, since the car is speeding up as it travels along the track.
However, it's worth noting that the answer could also be negative, depending on the direction of the acceleration. For example, if the car were to slow down, the acceleration would be negative.
Conclusion
In conclusion, we have used the formula for acceleration to solve a real-world problem involving a car racing on a track. We have shown that the acceleration of the car is 6 m/s^2, which is a positive value indicating that the car is speeding up.
Additional Examples
Here are a few additional examples of how to use the formula for acceleration:
- A car accelerates from 0 m/s to 25 m/s in 10 seconds. What is the acceleration?
- A ball is thrown upwards with an initial velocity of 10 m/s. It reaches a maximum height of 20 m in 2 seconds. What is the acceleration of the ball?
- A train accelerates from 50 m/s to 100 m/s in 5 seconds. What is the acceleration of the train?
Answer Key
A.
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.
Related Topics
- Velocity
- Speed
- Time
- Distance
- Force
- Newton's laws of motion