A driver in a car traveling at a speed of
56.6 mi/h sees a deer 106 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/s
change speed to m/s
then
Vf^2=Vi^2+2ad solve for a. d=106
To calculate the magnitude of the acceleration necessary for the car to stop just barely missing the deer, we need to use the kinematic equation of motion.
The equation we can use is:
v² = u² + 2as
where:
v = final velocity (0 m/s since the car needs to stop)
u = initial velocity (56.6 mi/h)
a = acceleration
s = distance (106 m)
First, we need to convert the initial velocity from miles per hour to meters per second (since the answer should be in m/s).
1 mile = 1.60934 kilometers
1 kilometer = 1000 meters
1 hour = 3600 seconds
So, the conversion is:
56.6 mi/h = 56.6 * 1.60934 * 1000/3600 m/s = 25.33 m/s (approximately)
Now, we can substitute the values into the equation:
0² = (25.33 m/s)² + 2a(106 m)
Expanding and rearranging the equation, we get:
0 = 642.0289 + 212a
Simplifying the equation:
212a = -642.0289
a = -642.0289 / 212
a ≈ -3.03 m/s²
The magnitude of the acceleration necessary for the car to stop just barely missing the deer is approximately 3.03 m/s². Note that the negative sign indicates that the acceleration is in the opposite direction of the initial motion (deceleration).