A person driving a car suddenly applies the brakes. The car takes 4s to come to rest while traveling 20 m at constant acceleration. Can the speed of the car immediately before the brakes were applied be determined without first determining the car's acceleration?

Yes, the speed of the car immediately before the brakes were applied can be determined without first calculating the acceleration. This can be done by using a kinematic equation that relates displacement, initial velocity, final velocity, and time directly.

We know the following:
- The displacement \( d = 20 \, \text{m} \)
- The final velocity \( v_f = 0 \, \text{m/s} \) (since the car comes to rest)
- The time taken \( t = 4 \, \text{s} \)

The kinematic equation we can use is:

\[
d = \frac{(v_i + v_f)}{2} \cdot t
\]

Where:
- \( d \) is the displacement
- \( v_i \) is the initial velocity (which is what we want to find)
- \( v_f \) is the final velocity
- \( t \) is the time

Since \( v_f = 0 \), the equation simplifies to:

\[
d = \frac{v_i}{2} \cdot t
\]

Solving for \( v_i \):

\[
v_i = \frac{2d}{t}
\]

Substitute the values:

\[
v_i = \frac{2 \times 20 \, \text{m}}{4 \, \text{s}} = \frac{40}{4} = 10 \, \text{m/s}
\]

So, the speed of the car immediately before the brakes were applied was \( 10 \, \text{m/s} \).

### Do you want more details, or have any further questions?

### Related Questions:
1. How can we determine the acceleration of the car during braking?
2. How much distance would the car travel if it took 6 seconds to stop instead of 4 seconds?
3. What kinematic equation would apply if the final velocity was not zero?
4. How would the result change if the car had traveled 30 meters instead of 20 meters before stopping?
5. Can we calculate the force exerted by the brakes if the mass of the car is known?

### Tip:
Always keep track of the known and unknown variables before selecting the appropriate kinematic equation.

Discover how to calculate the speed of a car before the brakes were applied, using kinematic equations. In this problem, the car comes to rest in 4 seconds after traveling 20 meters. This guide explains step-by-step how to find the initial speed without needing to calculate acceleration. Suitable for students in Grades 9-11.

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