A careless driver realizes they are about to hit an adorable puppy dog and hits their brakes, stopping over 61m in 4.8s. What was their initial velocity?

To find the initial velocity of the car, we can use the equation of motion for uniform acceleration. The driver stops in a distance of 61 meters over a time of 4.8 seconds, so the final velocity \( v_f \) is 0 m/s.

We'll use the following kinematic equation:

\[
v_f = v_i + a \cdot t
\]

Where:
- \( v_f \) is the final velocity (0 m/s),
- \( v_i \) is the initial velocity (what we are solving for),
- \( a \) is the acceleration, and
- \( t \) is the time (4.8 s).

To find \( a \), we use another equation:

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

Where:
- \( d \) is the distance (61 m),
- \( t \) is the time (4.8 s),
- \( v_i \) is the initial velocity, and
- \( a \) is the acceleration.

We'll first solve for \( a \), then use it to find \( v_i \). Let's calculate it.The initial velocity of the car was approximately \( 25.42 \, \text{m/s} \) before the driver applied the brakes.

Would you like more details on the calculation or explanation? 

Here are some related questions to further explore:
1. How do you calculate acceleration in this scenario?
2. What would happen if the car stopped in a shorter distance?
3. How does the stopping time affect the acceleration?
4. Can we calculate the force involved if we know the mass of the car?
5. What role does friction play in stopping the car?

**Tip:** When calculating initial velocities or accelerations, always check the given units (meters, seconds, etc.) to ensure consistency across all calculations.

Learn how to calculate the initial velocity of a car that stops over a distance of 61 meters in 4.8 seconds. This problem involves using kinematic equations of motion for uniformly accelerated motion, ideal for students in Grades 10-12.

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