How much time would it take a car, starting from rest, to travel 200 meters if it accelerates at a rate of 5 meters per second per second

We can solve this problem using the equation of motion:

\[
d = v_i t + \frac{1}{2} a t^2
\]

Where:
- \( d \) is the distance (200 meters),
- \( v_i \) is the initial velocity (0 since the car starts from rest),
- \( a \) is the acceleration (5 m/s²),
- \( t \) is the time (which we need to find).

Given that the car starts from rest, \( v_i = 0 \), so the equation simplifies to:

\[
d = \frac{1}{2} a t^2
\]

Substituting the known values:

\[
200 = \frac{1}{2} \times 5 \times t^2
\]

\[
200 = 2.5 \times t^2
\]

Solving for \( t^2 \):

\[
t^2 = \frac{200}{2.5} = 80
\]

Taking the square root of both sides:

\[
t = \sqrt{80} \approx 8.94 \, \text{seconds}
\]

Thus, it would take approximately **8.94 seconds** for the car to travel 200 meters.

Would you like more details or have any further questions?

Here are 5 related questions to explore:
1. How much distance would the car cover in the first 5 seconds?
2. What would the car’s final velocity be after traveling 200 meters?
3. How would the time change if the acceleration was doubled?
4. What formula would we use if the car had an initial velocity?
5. How long would it take the car to stop if it decelerated at the same rate?

**Tip:** When solving motion problems, ensure you correctly identify the initial conditions (such as initial velocity) before applying equations of motion.

How much time would it take a car, starting from rest, to travel 200 meters if it accelerates at a rate of 5 meters per second per second?

Learn how to calculate the time required for a car starting from rest to travel 200 meters with an acceleration of 5 m/s². This problem involves kinematics, quadratic equations, and the equations of motion, making it suitable for students in Grades 9-12.

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