Answer: The final velocity is 33.78 mi/h, so the driver did reduced his speed enough.
Explanation: The kinetic energy of an object can be calculated as:
K = (1/2)m*v^2
We know that the mass of the car is m=1100kg
and the initial velocity is 22m/s
The initial kinetic energy is:
K = (1/2)*1100*(22)^2 = 266,200 joules.
Now, if the kinetic energy decreases by 1.4x10^5 J, the new kinetic energy is:
K = 266,200j - 140,000j = 126,200j
So we now can find the new velocity in m/s.
126,200 = (1/2)*1100*v^2
126,200*2/1100 = v^2
229.45 = v^2
v = (229.45)^(1/2) = 15.1 m/s
We know that the limit is 35 mi/h, so we need to transform our result into miles per hour.
We know that in one hour, there are 3600 seconds, so the velocity per hour is:
15.1*3600 m/h = 54,360 m/h
and we know that one mile is 1609.34 meters, so we need to divide by 1609.34.
v = (54,360/1609.34) mi/h = 33.78 mi/h
this is less than the speed limit, so the driver reduced his speed enough.