hi.A vehicle weighing 1.3 tonne leaves skid marks 23 meters long.After 15 meters it hit pedestrain.The co efficient of friction is .7 .what was vehicle initial speed at start of skid and at impact.thanks
To find the initial speed of the vehicle at the start of the skid and at the point of impact, we can use the principles of motion and the concept of work done by friction.
Let's break down the problem step by step:
Step 1: Find the force of friction
The force of friction can be calculated using the formula:
force of friction = coefficient of friction * normal force
In this case, the normal force is equal to the weight of the vehicle, which is 1.3 metric tons (or 1300 kg) multiplied by the acceleration due to gravity (9.8 m/s^2), as the vehicle is not accelerating vertically. Thus, the normal force is:
normal force = weight = mass * gravity = 1300 kg * 9.8 m/s^2
Step 2: Find the work done by friction
The work done by friction can be calculated using the formula:
work done by friction = force of friction * distance
In this case, the distance is the length of the skid marks, which is 23 meters.
Step 3: Find the initial speed
Using the work-energy principle, the work done by friction is equal to the change in kinetic energy. Since the vehicle initially had no speed (at rest), the initial kinetic energy is zero. Therefore, the work done by friction is equal to the final kinetic energy.
The formula for kinetic energy is:
kinetic energy = 1/2 * mass * velocity^2
Since we are looking for the initial velocity, we can set up the equation as follows:
work done by friction = 1/2 * mass * (final velocity^2 - initial velocity^2)
Substituting the values for mass, the force of friction, and the distance, we can solve for the initial velocity.
This will give us the initial speed of the vehicle right at the beginning of the skid.
Step 4: Find the velocity at the point of impact
Since the vehicle skidded for an additional 15 meters after hitting the pedestrian, we can use the same equation as in Step 3 to find the velocity at the point of impact. However, this time, the distance will be 15 meters.
Substituting the values for mass, the force of friction, and the distance, we can solve for the final velocity.
This will provide us with the velocity of the vehicle at the point of impact with the pedestrian.
By following these steps, you can calculate the initial speed of the vehicle at the start of the skid and its speed at the point of impact. I hope this explanation helps you solve the problem effectively.