The table below shows how the braking distance x for a car depends on its initial speed u
u / ms-1 5.0 10 20 4
x / m 2.0 8.0 32 128
the reaction time of a driver is 0.60s. Calculate the sopping distance of the car when u= 30ms-1.
The mark scheme says:
Thinking distance= 30 X 0.6 =18m which I understand fully.
BRAKING DISTANCE =0.08 * U^2= 0.08 * 30^2= 72m IS THE BIT I DON’T UNDERSTAND. CAN SOMEONE PLEASE EXPALIN THE BRAKING DISTANCE STAGE AND WHY AND HOW YOU DO THIS BIT AS WELL AS ALL EQUATIONS INVOLVED!
Stopping distance= 18 +72= 90m which I understand fully.
please help.
To calculate the braking distance of a car, we can use the equation:
Braking Distance = 0.08 * u^2
where u is the initial speed of the car in meters per second (ms^-1). In your case, you want to calculate the braking distance when u = 30 ms^-1.
Let's break down the equation:
1. Convert the initial speed u to meters per second:
In this case, u is already given in ms^-1, so there is no need to convert it.
2. Square the initial speed:
We need to square the value of u. In this case, 30^2 = 900.
3. Multiply the squared speed by 0.08:
Multiply the squared speed by 0.08: 0.08 * 900 = 72.
So, when the initial speed of the car is 30 ms^-1, the braking distance is 72 meters.
The formula for braking distance is derived from experiments and observations. It is an approximation that represents the relationship between the initial speed of a car and the distance it takes to come to a complete stop when the brakes are applied. It takes into account factors such as the friction between the tires and the road surface, the weight of the car, and other factors. The specific value of 0.08 is a constant value derived from these observations.
In summary, to calculate the braking distance, you need to square the initial speed and multiply it by 0.08. Then, add the resulting value to the thinking distance to obtain the stopping distance.
To calculate the stopping distance of the car when u= 30 ms-1, we need to calculate the braking distance. The braking distance is given by the equation:
Braking distance = 0.08 * u^2
In this case, u = 30 ms-1.
Substituting this value into the equation, we have:
Braking distance = 0.08 * (30^2)
= 0.08 * 900
= 72 m
So, the braking distance is 72 m.
To calculate the stopping distance, we need to consider the thinking distance and the braking distance. The thinking distance, which is the distance traveled during the driver's reaction time, is calculated by multiplying the initial speed u by the reaction time (0.60 s in this case).
Thinking distance = u * reaction time
= 30 * 0.60
= 18 m
The stopping distance is then the sum of the thinking distance and the braking distance:
Stopping distance = thinking distance + braking distance
= 18 + 72
= 90 m
Therefore, the stopping distance of the car when u= 30 ms-1 is 90 m.