A driver in a car traveling at a speed of 55.3 mi/h sees a deer 108 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 not move in the meantime).
use the formula:
V^2 = U^2 + 2*a*s
here, V=0(final speed);
U= Initial speed (convert units mi/hr to m/s)
a = acceleration
s = 108 m
Find a in m/s^2 - your answer will be a negative value indicating deceleration.
To calculate the minimum constant acceleration needed for the car to stop without hitting the deer, we can use the kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity (which is 0, since the car needs to come to a stop)
u = initial velocity of the car (55.3 mi/h converted to m/s)
a = acceleration
s = distance covered (108 m)
First, let's convert the initial velocity from miles per hour (mi/h) to meters per second (m/s).
To convert from mi/h to m/s, we need to multiply the value by a conversion factor.
1 mi = 1609.34 m
1 h = 3600 s
So, the conversion factor is:
1 mi/h = 1609.34 m / 3600 s
Multiplying the initial velocity by the conversion factor, we get:
u = 55.3 mi/h * (1609.34 m / 3600 s) = 24.727 m/s (approximately)
Now, we can plug in the values into the kinematic equation:
0^2 = (24.727 m/s)^2 + 2a(108 m)
Simplifying the equation gives:
0 = 610.67 m^2/s^2 + 216a m
Rearranging the equation gives:
216a m = -610.67 m^2/s^2
Dividing by 216 m:
a = (-610.67 m^2/s^2) / (216 m)
Calculating the acceleration, we get:
a ≈ -2.83 m/s^2
Since acceleration cannot be negative in this context (we assumed the car is decelerating), the absolute value of the acceleration is:
|a| ≈ 2.83 m/s^2
Therefore, the minimum constant acceleration needed for the car to stop without hitting the deer is approximately 2.83 m/s^2.