A driver in a car traveling at a speed of

56 mi/h sees a deer 91.2 m away on the road.
Calculate the magnitude of the acceleration
necessary for the car to stop just barely missing the deer (assuming that the deer does not
move in the meantime)

To calculate the magnitude of the acceleration necessary for the car to stop just barely missing the deer, we can use the following kinematic equation:

v^2 = u^2 + 2as

Where:
v = final velocity (0 m/s, as the car needs to stop)
u = initial velocity (56 mi/h or 24.97 m/s)
s = displacement (91.2 m)
a = acceleration (unknown)

Rearranging the equation to solve for acceleration (a), we have:

a = (v^2 - u^2) / (2s)

Substituting the known values into the equation:

a = (0^2 - (24.97)^2) / (2 * 91.2)

a = -624.01 / 182.4

a ≈ -3.42 m/s^2

The magnitude of the acceleration necessary for the car to stop just barely missing the deer is approximately 3.42 m/s^2.

To calculate the magnitude of acceleration necessary for the car to stop just barely missing the deer, we can use the kinematic equation:

v^2 = u^2 + 2as

where:
v = final velocity (0 m/s, as the car needs to stop)
u = initial velocity (56 mi/h)
a = acceleration
s = distance (91.2 m)

However, we need to ensure that all units are consistent. Let's convert the initial velocity from miles per hour (mi/h) to meters per second (m/s).

1 mile = 1609.34 meters
1 hour = 3600 seconds

So, the initial velocity in meters per second:

u = 56 mi/h * (1609.34 m/1 mi) / (3600 s/1 h)
u = 56 * 1609.34 / 3600 m/s
u = 25.115 m/s (rounded to three decimal places)

Now, we can substitute the values into the kinematic equation:

0^2 = (25.115 m/s)^2 + 2a * 91.2 m

Simplifying the equation:

0 = 630.783225 + 182.4a

Rearranging to isolate the acceleration:

182.4a = -630.783225

a = -630.783225 / 182.4
a ≈ -3.46 m/s^2 (rounded to two decimal places)

Therefore, the magnitude of acceleration necessary for the car to just barely miss the deer is approximately 3.46 m/s^2. It should be noted that the negative sign indicates the deceleration or slowing down of the car.