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 determine the initial speed of the vehicle at the start of the skid and at the impact, we need to use the concept of conservation of momentum.
First, let's calculate the acceleration of the vehicle using the skid marks and the coefficient of friction.
The equation for the skid marks is given by:
\(s = \frac{{v_{\text{initial}}^2}}{{2a}}\)
where:
- s is the skid mark distance (23 meters),
- \(v_{\text{initial}}\) is the initial velocity (which we need to find),
- a is the acceleration.
Now, the coefficient of friction is given by:
\(f = \mu \cdot N\)
where:
- f is the frictional force,
- \(\mu\) is the coefficient of friction (0.7),
- N is the normal force.
The normal force can be calculated by multiplying the weight of the vehicle by the acceleration due to gravity (9.8 m/s^2).
\(N = \text{weight} \cdot g\)
Next, we can calculate the frictional force:
\(f = \text{frictional force} = \mu \cdot N\)
The frictional force is also equal to the mass of the vehicle times its acceleration:
\(f = m \cdot a\)
Now, we can combine the equations for frictional force:
\(\mu \cdot N = m \cdot a\)
\(\mu \cdot \text{weight} \cdot g = m \cdot a\)
We can rearrange the equation to solve for acceleration:
\(a = \frac{{\mu \cdot \text{weight} \cdot g}}{m}\)
Substituting the given values:
\(\mu = 0.7\),
weight = 1.3 tonne = 1300 kg,
g = 9.8 m/s^2,
we can find the value of acceleration.
Once you have the acceleration, we can substitute it back into the equation for the skid marks to find the initial velocity (\(v_{\text{initial}}\)).
Finally, to find the impact speed, we need to consider the conservation of momentum.
The equation for momentum is:
\(m_1 \cdot v_1 = m_2 \cdot v_2\)
where:
- m1 and m2 are the masses of the vehicle and the pedestrian (assume a reasonable value for the pedestrian),
- v1 is the initial velocity of the vehicle at the impact (which we need to find),
- v2 is the velocity of the pedestrian at the impact (which we assume to be 0).
Now you can solve the equation to find the initial velocity of the vehicle at the impact.
Remember to convert the weight from tonne to kg and use consistent units (meters and seconds) throughout the calculations.