A car moving at 50km/hr skids 15m with locked brakes. How far will the car skid (with locked brakes if the car moves at 100km/hr assume that the mass of the car is 500kg

if you double the speed, then distance quadruples.

To calculate how far the car will skid with locked brakes when it moves at 100km/hr, we can use the concept of kinetic energy and work done.

First, let's calculate the initial kinetic energy of the car when it moves at 50km/hr.

Given:
Initial velocity (v1) = 50km/hr = 13.89 m/s
Mass of the car (m) = 500kg

The formula for kinetic energy is:
Kinetic Energy (KE1) = (1/2) * m * v1^2

Plugging in the given values, we get:
KE1 = (1/2) * 500kg * (13.89 m/s)^2
KE1 = 96,548.05 Joules

Now, let's calculate the work done in stopping the car when it skids 15m with locked brakes.

Given:
Distance skidded (d1) = 15m

The formula for work done is:
Work (W1) = KE1 = (1/2) * m * v1^2

Plugging in the given values, we get:
W1 = (1/2) * 500kg * (13.89 m/s)^2
W1 = 96,548.05 Joules

Now, let's calculate the final kinetic energy of the car when it moves at 100km/hr.

Given:
Final velocity (v2) = 100km/hr = 27.78 m/s

The formula for kinetic energy is:
Kinetic Energy (KE2) = (1/2) * m * v2^2

Plugging in the given values, we get:
KE2 = (1/2) * 500kg * (27.78 m/s)^2
KE2 = 193,096.5 Joules

Finally, let's calculate the distance the car will skid with locked brakes when it moves at 100km/hr.

The formula for work done is:
Work (W2) = KE2 = (1/2) * m * v2^2

Plugging in the given values, we get:
W2 = (1/2) * 500kg * (27.78 m/s)^2
W2 = 193,096.5 Joules

Since work done (W2) remains constant, and the formula for work done is:
Work (W) = Force (F) * Distance (d)

We can rearrange the formula to solve for distance:
Distance (d2) = Work (W2) / Force (F)

Since the force (F) remains constant, the ratio of distances skidded to the initial kinetic energy is equal to the ratio of distances skidded to the final kinetic energy.

Therefore, the distance the car will skid (d2) when it moves at 100km/hr is:

d2 = (d1 * KE2) / KE1
d2 = (15m * 193,096.5 Joules) / 96,548.05 Joules
d2 = 30m

Therefore, the car will skid 30m with locked brakes when it moves at 100km/hr.

To determine how far the car will skid with locked brakes at a speed of 100 km/hr, we can use the concept of kinetic energy.

First, let's calculate the initial kinetic energy of the car at 50 km/hr:
Initial speed (v1) = 50 km/hr = 50,000 m/3600 s ≈ 13.89 m/s

Kinetic energy (KE1) = (1/2) * mass * velocity^2
= (1/2) * 500 kg * (13.89 m/s)^2
≈ 96,450 J

Next, let's determine the final kinetic energy of the car when it comes to a stop (with locked brakes).
Since the car comes to a stop, the final kinetic energy (KE2) will be zero.

Now, we can use the work-energy principle to find the distance the car will skid.
According to the work-energy principle, work done (W) on an object is equal to the change in its kinetic energy (ΔKE).

Work done (W) = ΔKE
W = KE2 - KE1

Since KE2 is zero, we have:
W = -KE1

The negative sign indicates that work is done against the direction of motion (opposite to the initial velocity).

Now, let's calculate the work done:
W = -(KE1)
= -(96,450 J)
= -96,450 J

Lastly, we can determine the distance (d) the car will skid using the formula:

Work done (W) = force (F) * distance (d)
-96,450 J = F * d

Since we are assuming the car's mass is 500 kg, the force (F) can be calculated using Newton's second law of motion:

Force (F) = mass (m) * acceleration (a)

We know the car's mass is 500 kg, and to find the acceleration (a), we can use the equation:

Final velocity (v2) = initial velocity (v1) + (2 * acceleration * distance)

Since the final velocity (v2) is zero when the car comes to a stop, we can rearrange the equation to solve for acceleration (a):

a = -v1^2 / (2 * d)

Plugging in the known values:
0 = (13.89 m/s)^2 / (2 * d)

After simplifying and rearranging, we find:
d = (13.89 m/s)^2 / (2 * a)

Now, let's calculate the acceleration (a):
v1 = 13.89 m/s
a = -v1^2 / (2 * d) = -(13.89 m/s)^2 / (2 * 15 m)

Plugging in the values and calculating:
a = -96.452 m/s^2

Finally, substituting the acceleration in the equation, we can calculate the distance (d):

d = (13.89 m/s)^2 / (2 * -96.452 m/s^2)
≈ 9.58 m

Therefore, the car will skid approximately 9.58 meters with locked brakes when it moves at 100 km/hr.