You're driving down the highway late one night at 20 m/s
 when a deer steps onto the road 60 m
 in front of you. Your reaction time before stepping on the brakes is 0.50 s
, and the maximum deceleration of your car is 10 m/s2. What is the maximum speed you could have and still not hit the deer?

To solve this problem, we need to break it into two phases:

1. **Phase 1: Reaction Time** - During the reaction time of 0.50 seconds, the car continues moving at a constant speed before the brakes are applied.
2. **Phase 2: Braking** - After the reaction time, the car decelerates at a rate of \( 10 \, \text{m/s}^2 \) until it comes to a stop.

### Step 1: Distance covered during reaction time
The car is moving at 20 m/s before the brakes are applied, and during the reaction time of 0.50 seconds, it travels a distance given by:
\[
d_{\text{reaction}} = v_{\text{initial}} \times t_{\text{reaction}}
\]
\[
d_{\text{reaction}} = 20 \, \text{m/s} \times 0.50 \, \text{s} = 10 \, \text{m}
\]

So, during the reaction time, the car travels 10 meters.

### Step 2: Remaining distance for braking
The total distance to the deer is 60 meters. After the reaction time, the remaining distance for braking is:
\[
d_{\text{braking}} = 60 \, \text{m} - 10 \, \text{m} = 50 \, \text{m}
\]

### Step 3: Maximum speed at which the car can stop within the remaining distance
Using the kinematic equation for deceleration:
\[
v_f^2 = v_i^2 + 2 a d
\]
where:
- \( v_f = 0 \, \text{m/s} \) (final velocity when the car stops),
- \( v_i \) is the initial velocity (the speed right before braking),
- \( a = -10 \, \text{m/s}^2 \) (deceleration),
- \( d = 50 \, \text{m} \) (remaining distance).

Rearranging the equation to solve for \( v_i \):
\[
0 = v_i^2 + 2(-10)(50)
\]
\[
v_i^2 = 1000
\]
\[
v_i = \sqrt{1000} \approx 31.62 \, \text{m/s}
\]

### Conclusion:
The maximum speed you could have and still not hit the deer is approximately **31.62 m/s**.

Would you like more details on any part of the solution?

Here are 5 related questions:
1. What would happen if the deceleration was less than 10 m/s²?
2. How would the result change if your reaction time was longer?
3. What if the deer was closer, say 40 m away instead of 60 m?
4. How does the braking distance depend on speed in general?
5. What if the road conditions made the deceleration less effective, like in rain?

**Tip:** Always be aware of the total stopping distance, which includes both the reaction distance and the braking distance.

You're driving down the highway late one night at 20 m/s when a deer steps onto the road 60 m in front of you. Your reaction time before stepping on the brakes is 0.50 s, and the maximum deceleration of your car is 10 m/s². What is the maximum speed you could have and still not hit the deer?

Solve a kinematics problem where a car traveling at 20 m/s needs to stop within 60 meters to avoid hitting a deer. Learn how to calculate the maximum speed using reaction time and deceleration, applying motion equations. Suitable for students in Grades 9-12.

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