a car is moving at speed of 50km/hr ,can be stopped by brake at least at 6 m.If the same car is moving at speed of 100 km/hr ,what is the minimum stopping distance?
To determine the minimum stopping distance of a car moving at a speed of 100 km/hr, we can use the concept of kinetic energy and the relationship between kinetic energy, mass, and velocity.
The kinetic energy of an object is given by the equation: KE = (1/2) * m * v^2
Where:
- KE represents the kinetic energy
- m represents the mass of the object
- v represents the velocity of the object
Assuming the mass of the car remains constant, the ratio of the kinetic energies can be expressed as:
(KE1 / KE2) = (v1^2 / v2^2)
Given that the car's speed doubles from 50 km/hr to 100 km/hr, the ratio of kinetic energies can be calculated as follows:
(KE1 / KE2) = (50^2 / 100^2) = 0.25
Now, let's calculate the minimum stopping distance at 50 km/hr using the information given. We can solve the equation:
KE = (1/2) * m * v^2
Rearranging the equation to solve for v:
v = √(2 * KE / m)
At 50 km/hr, the velocity can be calculated as follows:
v1 = √(2 * KE1 / m)
Next, let's substitute back into the kinetic energy equation to solve for KE1:
KE1 = (1/2) * m * v1^2
Given that the car can be stopped within 6 meters using the brake, we can set the equation as:
KE1 = (1/2) * m * v1^2 = (1/2) * m * (50 km/hr)^2
Now, let's calculate the minimum stopping distance at 100 km/hr using the calculated ratio of kinetic energies.
KE2 = KE1 * 0.25 = (1/2) * m * (50 km/hr)^2 * 0.25
Finally, we can find the minimum stopping distance at 100 km/hr using the equation for kinetic energy:
d = √(2 * KE2 / m)
Where:
- d represents the stopping distance
- KE2 represents the kinetic energy of the car at 100 km/hr
By plugging in the value of KE2 into the equation, we can calculate the minimum stopping distance at 100 km/hr.
Vf^2-Vi^2=2aS
a=acceleration/deceleration
Vf=final velocity = 0
Vi=initial velocity = 50 or 100
S=distance travelled.
By proportion, double the initial velocity, will quadruple the stopping distance, with the same Vf and a.