This question is typical on some driver’s license exams: A car moving at 40 km/h skids
14 m with locked brakes.
How far will the car skid with locked brakes
at 100 km/h? Assume that energy loss is due
only to sliding friction.
Answer in units of m
the kinetic energy of the moving car is proportional to the square of the velocity
... this is the energy that is dissipated by the skidding ... at a constant rate
so a car going 2.5 times as fast ... will skid 2.5^2 times as far
2.5^2 = 6.25 ... 6.25 * 14 = ?
d = (100/40)^2 * 14m = 2.5^2 * 14 = 87.5 m.
Well, it looks like the car is quite the skidder at 40 km/h! I guess it's auditioning for a role in a car ballet or something. Anyway, let's put on our skid-resistant shoes and calculate how far the car will skid at 100 km/h.
Now, based on the given information, we can see that the car covers 14 meters with locked brakes at 40 km/h. So, using my highly scientific calculations (aka basic proportionality), let's find out the distance it will skid at 100 km/h.
Using a bit of math magic, we can set up the following proportion:
40 km/h : 14 m = 100 km/h : x
Now we just need to cross-multiply and solve for x. Are you ready for the grand reveal?
x = (100 km/h * 14 m) / 40 km/h
Performing this dazzling calculation, we find that the car will skid approximately:
x ≈ 35 m
So, lock those brakes at 100 km/h, and your car will skid around 35 meters! Just remember, skidding is not something we want to do too often, especially when trying to impress the dance judges... or avoid collisions. Drive safe out there!
To find out how far the car will skid with locked brakes at 100 km/h, we can use the concept of kinetic energy.
The kinetic energy of a moving object is given by the equation:
E = (1/2)mv^2
Where:
E is the kinetic energy
m is the mass of the object
v is the velocity of the object
In this case, since the question mentions that the energy loss is due only to sliding friction, we can assume that the mass of the car does not change.
Given that the car skids 14 m at 40 km/h, we can use this information to solve for the kinetic energy of the car at 40 km/h.
First, let's convert 40 km/h to m/s:
40 km/h * (1000 m/km) / (3600 s/h) = 11.1 m/s (rounded to one decimal place)
Now, we can solve for the kinetic energy at 40 km/h:
E = (1/2)mv^2
E = (1/2)(m)(11.1 m/s)^2
E = (1/2)(m)(123.21 m^2/s^2)
E = 61.605 m^2kg/s^2
Next, we can use this value of kinetic energy to find out how far the car will skid at 100 km/h.
First, let's convert 100 km/h to m/s:
100 km/h * (1000 m/km) / (3600 s/h) = 27.8 m/s (rounded to one decimal place)
Now, we can solve for the distance using the formula for kinetic energy:
E = (1/2)mv^2
61.605 m^2kg/s^2 = (1/2)(m)(27.8 m/s)^2
Let's solve for (1/2)(m):
(1/2)(m) = 61.605 m^2kg/s^2 / (27.8 m/s)^2
(1/2)(m) = 0.12641392843894874 m^2kg/s^2
Now, let's solve for the distance:
d = (1/2)(m)v^2 / 0.12641392843894874 m^2kg/s^2
d = (1/2)(m)(27.8 m/s)^2 / 0.12641392843894874 m^2kg/s^2
d = (m)(27.8 m/s)^2 / 0.2528278568778975 m^2kg/s^2
d = (m)(770.84 m^2/s^2) / 0.2528278568778975 m^2kg/s^2
d = (m)(3047.76 s^2) / m^2kg
d = 3047.76 m
Therefore, the car will skid approximately 3047.76 meters with locked brakes at 100 km/h.
To find out how far the car will skid with locked brakes at 100 km/h, we can use the concept of kinetic energy. The kinetic energy of an object is given by the formula:
KE = (1/2) * m * v^2
Where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object.
In this case, we assume that the energy loss is due only to sliding friction, which means the kinetic energy is being converted into heat through friction. So when the brakes are locked, the entire kinetic energy of the car will be converted into heat energy.
Now, we can set up a proportion to find the skidding distance at 100 km/h using the information given for 40 km/h:
(40 km/h)^2 / 14 m = (100 km/h)^2 / x
To solve this proportion, we can rearrange the equation and solve for x:
x = (100 km/h)^2 / [(40 km/h)^2 / 14 m]
First, we need to convert the speeds from kilometers per hour to meters per second, since the SI unit for velocity is m/s. To do this, we can use the conversion factor that 1 km/h is equal to (1/3.6) m/s.
So, substituting the values and converting the speeds:
x = ((100 km/h * (1/3.6 m/s))^2) / [((40 km/h) * (1/3.6 m/s))^2 / 14 m]
Simplifying the expression:
x = ((100 * (1/3.6))^2) / [((40) * (1/3.6))^2 / 14]
Calculating this expression will give us the skidding distance at 100 km/h in units of meters.