A car moving at 15 m/s skids to a stop after 20 m. How far will it skid if it is moving at 45 m/s, assuming that the braking force is constant?
the kinetic energy (which must be dissipated by the braking force) is proportional to the square of the velocity
3 times the velocity means 9 times the stopping distance
Well, if the car is moving at 45 m/s, it will probably frighten all the skid marks on the road! But let's get serious for a second. If we assume that the braking force is constant, we can use the same equation as before to solve this problem.
We know that the car skids to a stop after 20 m when it's moving at 15 m/s. So, we can set up a ratio to find out how far it will skid when moving at 45 m/s.
The ratio is: (distance1 / velocity1) = (distance2 / velocity2)
Let's plug in the values: (20 m / 15 m/s) = (distance2 / 45 m/s)
Now, let's solve for distance2. Multiply both sides by 45 m/s:
distance2 = (20 m / 15 m/s) * 45 m/s
distance2 ≈ 60 m
So, if the car is moving at 45 m/s, assuming the braking force is constant, it will skid for approximately 60 meters.
Just make sure to leave enough space for all the skid marks! Safety first, my friend!
To find the distance the car will skid when moving at 45 m/s, we can use the concept of kinetic energy.
1. First, let's calculate the initial kinetic energy of the car when it is moving at 15 m/s. Kinetic energy (KE) is given by the formula:
KE = (1/2) * mass * velocity^2
Since the mass of the car is not provided, we can disregard it for this calculation.
KE = (1/2) * (15 m/s)^2
= (1/2) * (225 m^2/s^2)
= 112.5 Joules
2. Now that we have the initial kinetic energy, we know that the final kinetic energy will be zero (since the car comes to a stop). Using the same formula, we can find the distance (d) the car will skid when moving at 45 m/s.
KE = (1/2) * mass * velocity^2
0 = (1/2) * mass * (45 m/s)^2
Solving for mass:
mass = (0.5 * (45 m/s)^2) / (112.5 Joules)
mass = 0.5 * 2025 m^2/s^2 / 112.5 Joules
= 1012.5 kg
3. Now, we can find the distance (d) the car will skid when moving at 45 m/s using the formula for kinetic energy:
KE = (1/2) * mass * velocity^2
0.5 * 1012.5 kg * (45 m/s)^2 = (1/2) * 1012.5 kg * velocity^2
Solving for velocity:
d = (1/2) * 1012.5 kg * (45 m/s)^2 / (112.5 Joules)
= (1/2) * 1012.5 kg * 2025 m^2/s^2 / 112.5 Joules
= (1/2) * 2025 m^2/s^2
= 1012.5 m
Therefore, the car will skid a distance of 1012.5 meters when moving at 45 m/s, assuming that the braking force is constant.
To find out how far the car will skid when moving at 45 m/s, we can use the concept of kinetic energy.
When the car is skidding to a stop, the work done by the braking force is equal to the change in kinetic energy. Assuming that the braking force is constant, the work done can be expressed as the force multiplied by the distance.
Initially, the kinetic energy of the car is given by the equation:
KE = 0.5 * mass * velocity^2
Since we only want to find the change in distance, we can set up an equation by equating the initial kinetic energy of the car to the work done by the braking force.
Initially, the kinetic energy is:
KE1 = 0.5 * mass * (15 m/s)^2
When the car skids to a stop, the final kinetic energy is 0 because it has come to a complete stop. So, KE2 = 0.
Therefore, the work done by the braking force is equal to the change in kinetic energy, which can be calculated as:
Work = KE2 - KE1 = 0 - (0.5 * mass * (15 m/s)^2)
Now, we can find the constant braking force by dividing the work done by the distance:
Force = Work / Distance
Since the braking force is constant, it can be expressed as:
Force = mass * acceleration
Equating the two expressions for the force, we have:
mass * acceleration = Work / Distance
We can rearrange this equation to solve for the acceleration:
acceleration = (Work / Distance) / mass
Since the acceleration is constant, we can use it to find the distance traveled when the car is moving at 45 m/s:
Distance = (0.5 * mass * (45 m/s)^2) / acceleration
So, by substituting the values we know into the equation, we can determine the distance the car will skid when moving at 45 m/s.