A driver in a car traveling at a speed of
62 mi/h sees a deer 112 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).
Answer in units of m/s2
To calculate the magnitude of the acceleration necessary for the car to stop just barely missing the deer, we can first convert the speed of the car from miles per hour (mi/h) to meters per second (m/s).
1 mile = 1609.34 meters
1 hour = 3600 seconds
So, the speed of the car in meters per second is:
62 mi/h * (1609.34 m/1 mi) * (1 h/3600 s) = 27.734 m/s (rounded to three decimal places)
Now, let's calculate the deceleration needed to stop the car just before hitting the deer.
The initial velocity of the car, u, is 27.734 m/s.
The final velocity of the car when it stops, v, is 0 m/s.
The distance traveled by the car, s, is 112 m.
Using the kinematic equation:
v^2 = u^2 + 2as
Rearranging the equation to solve for acceleration, a, we have:
a = (v^2 - u^2) / (2s)
Plugging in the values:
a = (0^2 - 27.734^2) / (2 * 112)
a = -767.356 / 224
a = -3.427 m/s^2
Since the sign is negative, it indicates that the car needs to accelerate in the opposite direction (decelerate) with a magnitude of 3.427 m/s^2 in order to stop just before hitting the deer.
Therefore, the magnitude of the acceleration necessary for the car to stop just barely missing the deer is 3.427 m/s^2.
To find the magnitude of the acceleration necessary for the car to stop just barely missing the deer, we can use the following steps:
Step 1: Convert the speed of the car from miles per hour (mi/h) to meters per second (m/s).
1 mile = 1609.34 meters
1 hour = 3600 seconds
So, 62 mi/h = (62 * 1609.34) meters / (3600 seconds) = 27.78 m/s
Step 2: Write down the given values:
Initial velocity (u) = 27.78 m/s (speed of the car)
Final velocity (v) = 0 m/s (car needs to stop)
Distance (s) = 112 m (distance between the deer and the car)
Step 3: Use the following kinematic equation to find the acceleration (a):
v^2 = u^2 + 2as
Rearrange the equation to solve for acceleration (a):
a = (v^2 - u^2) / 2s
Substitute the values:
a = (0 - 27.78^2) / (2 * 112)
a = (-771.8884) / 224
a ≈ -3.448 m/s^2
Since we are only looking for the magnitude of the acceleration (acceleration is a vector), the magnitude is given by the absolute value of the calculated result:
|a| ≈ |-3.448| ≈ 3.448 m/s^2
Hence, the magnitude of the acceleration necessary for the car to stop just barely missing the deer is approximately 3.448 m/s^2.