a car moving at 15 meters per second skids to a stop in 20 meters. if the car travels at 45 meters per second, how far will it skid, assuming the same constant braking force
The skid distance is proportional to the square of the initial velocity.
The initial velocity is tripled. What happens to the square of velocity?
To determine how far the car will skid when traveling at 45 meters per second, assuming the same constant braking force, we can use the concept of kinetic energy.
1. First, let's calculate the initial kinetic energy of the car when it is traveling at 15 meters per second. The formula for kinetic energy is:
Kinetic Energy = (1/2) * mass * velocity^2
Since the mass of the car doesn't change, we don't need to consider it in our calculations.
Initial Kinetic Energy = (1/2) * 15^2
2. Next, let's calculate the final kinetic energy when the car comes to a stop. The final kinetic energy will be zero since the car is no longer in motion.
Final Kinetic Energy = 0
3. Now, let's find the change in kinetic energy. The change in kinetic energy is given by the difference between the initial and final kinetic energy.
Change in Kinetic Energy = Final Kinetic Energy - Initial Kinetic Energy
Change in Kinetic Energy = 0 - Initial Kinetic Energy
4. The change in kinetic energy is equivalent to the work done by the braking force in bringing the car to a stop. Therefore, we can equate the change in kinetic energy to the work done:
Change in Kinetic Energy = Work Done
Work Done = Change in Kinetic Energy
5. We can then use the work-energy principle to relate the work done by the braking force to the distance over which the car skids:
Work Done = Force * Distance
6. Since the braking force is assumed to be constant, the work done by the braking force is also constant. Therefore, we can set up the following equation:
Change in Kinetic Energy = Constant Force * Distance
7. Now, let's substitute the respective values into the equation:
0 - Initial Kinetic Energy = Constant Force * Distance
8. Rearranging the equation, we can solve for the distance:
Distance = (0 - Initial Kinetic Energy) / Constant Force
9. Plug in the values for the initial kinetic energy and solve for distance:
Distance = (0 - [(1/2) * 15^2]) / Constant Force
10. Now, let's use the distance obtained in step 9 to calculate the distance when the car is traveling at 45 meters per second:
Distance = (0 - [(1/2) * 45^2]) / Constant Force
So, to find out how far the car will skid when traveling at 45 meters per second, we first need to determine the value of the constant braking force. Once we know the braking force, we can use the formula derived above to calculate the distance.