What is the final velocity of a car that accelerated 10 m/s^2 from rest and traveled 180m

We can solve this problem using the kinematic equation:

\[
v_f^2 = v_i^2 + 2a d
\]

where:
- \(v_f\) is the final velocity (what we're solving for),
- \(v_i\) is the initial velocity (given as 0 m/s, since the car starts from rest),
- \(a\) is the acceleration (given as 10 m/s²),
- \(d\) is the distance traveled (given as 180 m).

Let's substitute the known values into the equation:

\[
v_f^2 = 0^2 + 2(10 \, \text{m/s}^2)(180 \, \text{m})
\]

\[
v_f^2 = 3600 \, \text{m}^2/\text{s}^2
\]

Now, take the square root of both sides:

\[
v_f = \sqrt{3600 \, \text{m}^2/\text{s}^2}
\]

\[
v_f = 60 \, \text{m/s}
\]

So, the final velocity of the car is **60 m/s**.

Would you like a more detailed explanation or further clarification?

Here are five related questions you might find interesting:
1. How would the final velocity change if the car accelerated at 20 m/s² instead of 10 m/s²?
2. What is the time it took for the car to travel 180 meters with the same acceleration?
3. How much distance would the car cover if it accelerated at 10 m/s² for 10 seconds?
4. What is the kinetic energy of the car at 60 m/s if it has a mass of 1000 kg?
5. What would happen to the final velocity if the car had an initial velocity of 10 m/s?

**Tip:** Always keep track of your initial conditions in kinematic problems; starting velocity is crucial when solving for motion-related variables.

What is the final velocity of a car that accelerated 10 m/s^2 from rest and traveled 180m?

Discover how to calculate the final velocity of a car that accelerates at 10 m/s² from rest and travels 180 meters. Using kinematic equations of motion, this solution explains step-by-step how to find the final velocity of the car, making it suitable for students in Grades 9-11.

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