A car initially at rest accelerates at 10
g2 . The car's speed after it has traveled 25 meters is most nearly What?

To solve this, we can use the kinematic equation that relates initial velocity, acceleration, displacement, and final velocity:

\[
v^2 = u^2 + 2as
\]

Where:
- \(v\) is the final velocity (which we are trying to find),
- \(u\) is the initial velocity (which is 0, since the car starts from rest),
- \(a\) is the acceleration,
- \(s\) is the displacement (distance traveled).

### Given dataTo solve this, we can use the kinematic equation that relates initial velocity, acceleration, displacement, and final velocity:

\[
v^2 = u^2 + 2as
\]

Where:
- \(v\) is the final velocity (which we are trying to find),
- \(u\) is the initial velocity (which is 0, since the car starts from rest),
- \(a\) is the acceleration,
- \(s\) is the displacement (distance traveled).

### Given 
- \(u = 0\) m/s (initial velocity),
- \(a = 10 \, \text{m/s}^2\) (acceleration),
- \(s = 25 \, \text{m}\) (displacement).

We plug the values into the equation:

\[
v^2 = 0^2 + 2 \times 10 \, \text{m/s}^2 \times 25 \, \text{m}
\]

\[
v^2 = 500 \, \text{m}^2/\text{s}^2
\]

\[
v = \sqrt{500} \approx 22.36 \, \text{m/s}
\]

So, the car's speed after traveling 25 meters is approximately **22.36 m/s**.

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the speed of the car after 50 meters?
2. How long does it take the car to travel 25 meters?
3. How does the acceleration affect the speed if the car accelerates faster?
4. What if the initial speed of the car is not zero?
5. How can we find the time taken if we only know the final speed?

**Tip:** Always check if the initial velocity is zero, as it simplifies many kinematic equations.

A car initially at rest accelerates at 10 m/s². The car's speed after it has traveled 25 meters is most nearly what?

Learn how to calculate the final speed of a car initially at rest, accelerating at 10 m/s² over 25 meters using the kinematic equation v^2 = u^2 + 2as. This problem is ideal for students in Grades 9-12 studying kinematics.

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