A car moving with a speed of 50 km/h, can be stopped by brakes after at least 6m. If the same car is moving at a speed of 100 km/h, the minimum stopping distance is [AIEEE 2003]a)12 mb)18 mc)24 md)6 mCorrect answer is option 'C'. Can you explain this answer?

Question

A car moving with a speed of 50 km/h, can be stopped by brakes after at least 6m. If the same car is moving at a speed of 100 km/h, the minimum stopping distance is        [AIEEE 2003]a)12 mb)18 mc)24 md)6 mCorrect answer is option 'C'. Can you explain this answer?

Answer

We know that retardation of a car with an initial speed of 50kmph stops after 6 m.
We know that v² - u² = 2as (third equation of motion)
► 0 - 50² = 2 * a * 6
► a = - 50² / 12
Hence when the initial speed is 100 kmph
We get,
► -100² = 2 * a * s
► 2 * s = 12 * (100² / 50²)
Thus we get s = 24 m.

Answer

Answer

Answer

HEY.
DEAR.
IF V = 2V
THEN STOPPING DISTANCE IS
4 TIMES OF PREVIOUS VALUE.
SO
OPTION C.
IF YOU HAVE ANY QUERY ASK

Answer

ANSWER 24 m$ units of distance in km.   u = 50 km/h  v = 0  due to retardation a = -a s = 6m = 6/1000 km = 0.006km USING (v)^2 = (u)^2 + 2as, we get, # 0 = (50)^2 + 2(-a)0.006 # -2500 = -2a × 0.006 # (2500 × 1000)/12 = a Again, using (v)^2 = (u)^2 + 2as, we get, # 0 = (100)^2 - 2{(2500 × 1000)/12}s # (10000 × 6) / (2500 × 1000) = s # s = 6/250 km # s = 0.024 km # s = 24 m

Answer

Given:
Speed of the car = 50 km/h
Stopping distance at this speed = 6 m

To find:
Minimum stopping distance when the car is moving at a speed of 100 km/h

Solution:
We can solve this problem using the concept of kinetic energy.

1. Understanding the concept of kinetic energy:
When an object is in motion, it possesses kinetic energy. The kinetic energy (KE) of an object is given by the equation KE = 0.5 * m * v^2, where m is the mass of the object and v is its velocity.

2. Relationship between kinetic energy and stopping distance:
The stopping distance of a car is directly proportional to its kinetic energy. This means that if the kinetic energy of the car is doubled, the stopping distance will also double.

3. Calculating the kinetic energy of the car at a speed of 50 km/h:
The speed of the car is given as 50 km/h. To calculate the kinetic energy, we need to convert it to m/s. We know that 1 km/h = 0.27778 m/s.
So, the speed of the car in m/s = 50 km/h * 0.27778 m/s = 13.89 m/s.

Using the formula KE = 0.5 * m * v^2, we can calculate the kinetic energy. Let's assume the mass of the car to be 'm'.
KE = 0.5 * m * (13.89)^2

4. Using the concept of kinetic energy to find the minimum stopping distance at a speed of 100 km/h:
Now we need to find the minimum stopping distance when the car is moving at a speed of 100 km/h.

The speed of the car in m/s = 100 km/h * 0.27778 m/s = 27.78 m/s.

Using the formula KE = 0.5 * m * v^2, we can calculate the kinetic energy. Let's assume the mass of the car to be 'm'.
KE = 0.5 * m * (27.78)^2

As mentioned earlier, the stopping distance is directly proportional to the kinetic energy. Therefore, the minimum stopping distance at a speed of 100 km/h will be twice the stopping distance at a speed of 50 km/h.

Minimum stopping distance = 2 * 6 m = 12 m.

Therefore, the correct answer is option 'C' - 24 m.

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