Respuesta :
Answer:
skid distance = 180 m
Explanation:
given,
mass of the car = 1000 Kg
speed of the car = 40 Km/hr
distance to stop = 20 m
if speed is now = 120 Km/he
distance to stop = ?
from given question we can state that,
Work done by the friction is equal to the change in kinetic energy of the car.
[tex]W= \dfrac{1}{2}mv^2[/tex]............(1)
And we also know that work is directly proportional to displacement
W = F × x...........................(2)
from the equation (1) and (2)
x ∝ v²
now,
here velocity is increased from 40 km/h to 120 km/h means velocity is increase 3 times
so displacement will be equal to 3² or 9 times
hence, skid distance will be equal to 9 x 20 = 180 m
skid distance = 180 m
To solve the problem we must know about the third equation of motion.
What is the third equation of motion?
We know that the third equation of motion is given as,
[tex]v^2 -u^2 = 2as[/tex]
where v is the final velocity, u is the initial velocity, a is the acceleration and s is the displacement.
The distance traveled for which the car will skid is equal to 180 m.
What is the deceleration of the car?
We will first calculate the deceleration that will cause the car to stop, for that we will use the third equation of motion,
[tex]v^2 -u^2 = 2as[/tex]
As it is already given to us the following values,
Initial velocity of the car, v = 40 km/hr = 11.1111 m/s
Final velocity of the car, u = 0 m/s (rest)
distance traveled by car, s = 20 meters
Substitute them in the equation,
[tex]0^2 -(11.1111)^2 = 2a(20)\\\\a = -3.08642\rm\ m/s^2[/tex]
Hence, the deceleration of the car will be equal to -3.08642 m/s².
What is the distance for which car will skid?
Now, the distance for which the car will skid can be calculated by the third equation of motion.
Given to us
Initial velocity of the car, v = 120 km/hr = 33.3334 m/s
Ffinal velocity of the car, u = 0 m/s (rest)
Subsitute the values,
[tex]v^2 -u^2= 2as\\\\0^2 -33.3334^2 = 2(-3.08642)s\\\\s = 180\rm\ m[/tex]
Hence, the distance traveled for which the car will skid is equal to 180 m.
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