Respuesta :
Answer:
150 m
Explanation:
Distance traveled during reaction time = .5 x 30 = 15 m
Actual distance during which there was deceleration = 60 - 15 = 45 m .
force x displacement = kinetic energy
F x s = 1/2 m v² ;
F x 45 = 1/2 m 30² = 450 m ----( 1 )
for second case
Fx S = 1/2 m 50² = 1250 m --------( 2 )
Dividing( 1 )and ( 2 )
S/45 = 1250 /450 = 125 / 45
S = 125 m
Add distance traveled in reaction time in second case = 50 x .5 = 25 m
total distance required = 25 + 125 = 150 m
The minimum stopping distance for the car which travels with speed of 50 m/s is 125 meters.
What is work energy theorem?
According to the work energy theorem, the sum of all the forces acting on a body to do a work is equal to the change in the kinetic energy of the body.
Here, in the problem the speed of the car is 30 m/s and the reaction time is  0.5 seconds. Thus the distance traveled in the driver's reaction time is,
[tex]s=30\times0.5\\s=15\rm m[/tex]
The total distance traveled during the declaration is,
[tex]x=60-15\\x=45\rm m[/tex]
As the speed of the car is 30 m/s. Thus, using the above formula, we get,
[tex]F\times45=\dfrac{1}{2}m\times30^2\\\dfrac{F}{m}=10[/tex]
Now the speed of the car is 50 meter per second. Suppose the minimum stopping distance for the same car is (x) meters. Thus using the above formula we get,
[tex]F\times x=\dfrac{1}{2}m\times50^2\\\dfrac{F}{m}=\dfrac{1250}{x}[/tex]
Compare the values of F/m from both equations, we get,
[tex]\dfrac{1250}{x}=10\\x=125\rm m[/tex]
Thus the minimum stopping distance for the car traveling at a speed of 50 m/s is 125 meters.
Learn more about the work energy theorem here;
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