A driver in a car traveling at a speed of 60 mi/h sees a deer 100 m away on the road. Calculate the minimum constant acceleration that is necessary for the car to stop without hitting the deer (assuming that the deer does no move in the meantime).

Work (so far):
100 m x 1 km/1000 m x .621 mi/km =0.0621 mi

Answer (back of the book): -3.60 m/s^2

60 mph = 88 ft/s = 26.82 m/s

To decelerate from 26.82 m/s to 0 in 100 m, the time of travel will be
(100 m)/(average speed) = 100/13.41= 7.46 s. The deceleration rate is 26.82 m/s/7.46 s = -3.59 m/s^2
Since there are only two significand figures ikn this problem, it should be rounded to -3.60 m/s^2.

Well, let's see if I can put a funny spin on this physics problem!

So, the deer is just chillin' on the road 100 meters away, probably practicing its dance moves or something. Now, the driver doesn't want to crash into Bambi (that would be a really bad ending for everyone involved), so they need to stop the car in time.

Now, to figure out the minimum constant acceleration needed to stop the car without hitting the deer, we need to do a little math. We converted the distance to miles, which is 0.0621 mi. But since the speed is given in mi/h (miles per hour), we need to convert the speed too.

So, let's take a moment to appreciate the fact that we have to convert miles to meters and hours to seconds. Physics, seriously, why you gotta make things so complicated?

Anyways, after doing all the unit conversions, we end up with an acceleration value of -3.60 m/s^2. And that's the magical number! If the driver accelerates with at least that much of a negative acceleration (which means slowing down, in case you're not up to snuff on physics lingo), they can stop the car in time and avoid turning Bambi into roadkill.

So there you have it, folks! The minimum constant acceleration needed is -3.60 m/s^2. Don't forget to carry that negative sign with you, otherwise you might just hit the deer and send him straight to the "Last Dance" party in the sky.

To solve this problem, we can use the equations of motion.

Step 1: Convert the speed of the car to meters per second.
Given: Speed of the car = 60 mi/h
Conversion: 60 mi/h * 1.6 km/mi * 1000 m/km * 1 h/3600 s = 26.67 m/s

Step 2: Determine the initial velocity (u) and final velocity (v) of the car.
Given: u = 26.67 m/s (initial velocity, since the car is initially moving)
Required: v = 0 m/s (final velocity, since the car needs to stop)

Step 3: Determine the distance (s) covered by the car.
Given: Distance = 100 m

Step 4: Use the equation of motion to calculate the required acceleration (a).
v^2 = u^2 + 2as

Substituting the given values:
0 = (26.67 m/s)^2 + 2a * 100 m

Step 5: Solve for acceleration (a).
a = - (26.67 m/s)^2 / 2 * 100 m
a = - 355.56 m^2/s^2 / 200 m
a = -1.78 m/s^2

Therefore, the minimum constant acceleration required for the car to stop without hitting the deer is -1.78 m/s^2.

The answer given in the back of the book (-3.60 m/s^2) is incorrect based on the information provided.

To calculate the minimum constant acceleration required for the car to stop without hitting the deer, we can use the following steps:

1. Convert the speed of the car from miles per hour to meters per second since the distance to the deer is given in meters and acceleration is typically measured in meters per second squared.
- 60 mi/h x 1.609 km/mi x 1000 m/km x 1 h/3600 s ≈ 26.82 m/s

2. Next, we can use the equation of motion to find the minimum constant acceleration needed to stop the car.
- The equation of motion we will use is: v² = u² + 2as
- Here, v is the final velocity (0 m/s as the car needs to stop), u is the initial velocity (26.82 m/s), a is the acceleration, and s is the distance (100 m).

3. Rearrange the equation to solve for the acceleration (a):
- 0² = (26.82 m/s)² + 2a(100 m)
- 0 = 718.92 m²/s² + 200a

4. Solve for the acceleration (a):
- Rearrange the equation to isolate a:
- 200a = -718.92 m²/s²
- Divide both sides by 200:
- a ≈ -3.5956 m/s²

Therefore, the minimum constant acceleration required for the car to stop without hitting the deer is approximately -3.60 m/s². The negative sign indicates that the acceleration is in the opposite direction of the car's initial velocity, as it needs to decelerate to come to a stop.