Omar Alawad
Math SL
Mr. Sidat
Stopping distance
Introduction
When driving on roads, drivers may see an obstacle ahead that requires them to apply brakes suddenly to stop. The distance covered by the car from the moment the driver applied brakes to the moment the car stops is called the stopping distance, which is also referred to as the braking distance. For a car travelling at an initial speed of , the stopping distance traveled by this car is given in the formula: The stopping distance is directly proportional to the square of the speed of the car, just before the brakes got applied i.e. By introducing a constant of proportionality to the above equation, we obtain the general term for the braking distance. The value of the …show more content…
Applying this fact to the equation above, and replacing with , we obtain the simple formula of stopping distance. Data collected
The stopping distance of five different cars is presented in the table below. The brakes were applied when the travelling speed of the cars reached 100km/h.
Type of car Stopping distance (m)
Ferrari 550 Maranello
Lexus LS400
Mercedes C36
Nissan 200SX
Toyota Corolla 41.5
55.9
44.4
47.8
68.9
By manipulating the stopping distance equation, the deceleration formula becomes;
By applying the same process to the other values we obtain the table below:
Type of car Stopping distance (m) Deceleration ( )
Ferrari 550 Maranello
Lexus LS400
Mercedes C36
Nissan 200SX
Toyota Corolla 41.5
55.9
44.4
47.8
68.9 9.297
6.902
8.689
8.071
5.600
From the data above, it is clear that the shorter is the stopping distance the larger is the deceleration.
Speed during breaking
An interesting case to analyze is the movement of the car after applying the brakes. From the equation of linear motion used earlier, we make the subject of the formula since it is the variable of interest.
We only focus on the positive values of v.
The rate at which changes on the distance travelled ( ) …show more content…
It is interesting to study the behavior of the vehicle after the application of brakes, until it comes to a halt. For this case, we analyze how a car will behave when stopping from a speed of 100 km/h. We make an assumption that the car decelerates at a constant rate of
However, the value of when the car comes to a halt. Making the change in the above equation and making the subject:
We now focus our attention on the speed of the car at different distances measured from the time of braking. The considered braking is from a speed of 100km/h,
For example, when we get
The table below shows different values of speed at various distances
Distance (meters) Speed (km/h)
0
5
10
15
20
25
30
35
38.58 100
93.3
86.1
78.2
69.4
59.3
47.2
30.5
0
A closer analysis of the data in the table, at 35 meters, the car, is still moving at 30.5 km/h. The speed is quite high given the fact that the car stops 3.5 meters further from this point. Using the data to plot a chart speed against distance travelled from the point when the brakes got applied, we come up with the figure
Math SL
Mr. Sidat
Stopping distance
Introduction
When driving on roads, drivers may see an obstacle ahead that requires them to apply brakes suddenly to stop. The distance covered by the car from the moment the driver applied brakes to the moment the car stops is called the stopping distance, which is also referred to as the braking distance. For a car travelling at an initial speed of , the stopping distance traveled by this car is given in the formula: The stopping distance is directly proportional to the square of the speed of the car, just before the brakes got applied i.e. By introducing a constant of proportionality to the above equation, we obtain the general term for the braking distance. The value of the …show more content…
Applying this fact to the equation above, and replacing with , we obtain the simple formula of stopping distance. Data collected
The stopping distance of five different cars is presented in the table below. The brakes were applied when the travelling speed of the cars reached 100km/h.
Type of car Stopping distance (m)
Ferrari 550 Maranello
Lexus LS400
Mercedes C36
Nissan 200SX
Toyota Corolla 41.5
55.9
44.4
47.8
68.9
By manipulating the stopping distance equation, the deceleration formula becomes;
By applying the same process to the other values we obtain the table below:
Type of car Stopping distance (m) Deceleration ( )
Ferrari 550 Maranello
Lexus LS400
Mercedes C36
Nissan 200SX
Toyota Corolla 41.5
55.9
44.4
47.8
68.9 9.297
6.902
8.689
8.071
5.600
From the data above, it is clear that the shorter is the stopping distance the larger is the deceleration.
Speed during breaking
An interesting case to analyze is the movement of the car after applying the brakes. From the equation of linear motion used earlier, we make the subject of the formula since it is the variable of interest.
We only focus on the positive values of v.
The rate at which changes on the distance travelled ( ) …show more content…
It is interesting to study the behavior of the vehicle after the application of brakes, until it comes to a halt. For this case, we analyze how a car will behave when stopping from a speed of 100 km/h. We make an assumption that the car decelerates at a constant rate of
However, the value of when the car comes to a halt. Making the change in the above equation and making the subject:
We now focus our attention on the speed of the car at different distances measured from the time of braking. The considered braking is from a speed of 100km/h,
For example, when we get
The table below shows different values of speed at various distances
Distance (meters) Speed (km/h)
0
5
10
15
20
25
30
35
38.58 100
93.3
86.1
78.2
69.4
59.3
47.2
30.5
0
A closer analysis of the data in the table, at 35 meters, the car, is still moving at 30.5 km/h. The speed is quite high given the fact that the car stops 3.5 meters further from this point. Using the data to plot a chart speed against distance travelled from the point when the brakes got applied, we come up with the figure