A car is traveling at 80 miles per hour down a paved, asphalt road in good condition. The driver steps on the brake, decelerating at a constant rate (expressed in m/s^2), to avoid hitting a horse in the road 1500 feet away. If the driver does not wish to experience too rapid a deceleration, in other words, a deceleration greater than -2g’s or -2 x 9.8 m/s^2 to avoid skidding or possible bodily injury, and is only able to decelerate in a straight line, how long does it take the driver to stop? Can a collision with the horse be avoided? Note: Convert all variables to the metric (mks) system before performing your calculations.
vf^2=vi^2+2ad
1500ft=457m
80mph=35.7m/s
0^2=35.7^2+2a(457) solve for a. Is it less than 2g?
So it would be ....
0=1274.49+2a(457)
O=1274.49+914a?
Yes? No?
To solve this problem, we need to convert the given values to the metric system (mks), as you mentioned:
Distance to the horse = 1500 feet
Since 1 foot is approximately 0.305 meters, the distance to the horse in the metric system is:
Distance = 1500 ft * 0.305 m/ft = 457.2 meters
Initial velocity (v0) of the car = 80 miles per hour
Since 1 mile is approximately 1.60934 kilometers, and 1 hour is exactly 3600 seconds, we can convert the velocity to meters per second:
v0 = 80 miles/hour * (1.60934 km/mile) * (1000 m/km) * (1 hour/3600 seconds) = 35.76 m/s
Maximum deceleration = -2g's or -2 x 9.8 m/s^2
We can directly use -2g's for deceleration value, which is -2 x 9.8 m/s^2 = -19.6 m/s^2
Now that we have converted the values, we can solve the problem using the equations of motion.
The equation that relates distance (d), initial velocity (v0), final velocity (v), and acceleration (a) is:
d = (v^2 - v0^2) / (2a)
In this case, the distance is 457.2 meters, the initial velocity is 35.76 m/s, and the acceleration is -19.6 m/s^2 (deceleration as negative).
Plugging these values into the equation, we get:
457.2 = (v^2 - 35.76^2) / (2 * -19.6)
Simplifying the equation:
457.2 = (v^2 - 1278.1776) / -39.2
-39.2 * 457.2 = v^2 - 1278.1776
-17909.44 = v^2 - 1278.1776
v^2 = -17909.44 + 1278.1776
v^2 = -16631.2624
v = √(-16631.2624)
We have a problem here. The final answer for v comes out as an imaginary number (√ of a negative value), which doesn't make sense in this case. Thus, it is not possible for the car to stop in time to avoid a collision with the horse.