Final answer:
To calculate the length of skid marks made by a car when braking, you first convert the car's initial speed to meters per second, then compute the car's deceleration and use the kinematic equation for uniform acceleration to find the stopping distance.
Step-by-step explanation:
The student is asking about the calculation of skid mark length when a car traveling at a certain speed comes to a stop due to braking. To find the length of the skid marks, you need to calculate the stopping distance using the initial speed and the duration of deceleration.
To calculate this, we use the kinematic equation for uniform acceleration, which in this case is deceleration:
s = ut + ½at²
where:
- s is the stopping distance or displacement (the length of the skid marks)
- u is the initial velocity (110 km/hr or approximately 30.56 m/s)
- t is the time taken to stop (4.5 s)
- a is the acceleration, which will be a negative value since the car is decelerating
First, we need to convert the speed from km/hr to m/s:
110 km/hr × (1000 m/km) / (3600 s/hr) ≈ 30.56 m/s
Since the car comes to a complete stop, the final velocity v = 0 m/s. We can then use the equation v = u + at to find the acceleration:
0 = 30.56 + a × 4.5
This gives us a = -6.79 m/s² (negative because it is deceleration). Now we can plug this into the displacement formula:
s = (30.56 m/s) × 4.5 s + ½(-6.79 m/s²)(4.5 s)²
This calculation will yield the length of the skid marks, which is the answer the student is looking for.