2. Stopping Distance and Reaction Time

3. The driver in the car B sees the man A 40 m away at time t = 0. The velocity of the car changes according to the graph below.

4. Will the car B collide with the man A ?

5. Reaction Time =0.5 s From t = 0 s to t = 0.5 s, the driver is thinking what to do. He does not apply the brakes during this period. Area = 10 m. It is the distance travelled by the car when the driver is thinking. This is known as thinking distance.

7. Braking Time = 2.5 s From t = 0.5 s to t = 3 s,the brakes are applied. The car slows down until it stops at t = 3 s. Area = 25 m. It is the distance travelled by the car during braking. This is known as braking distance.

8. Braking Time = 2.5 s Area = 25 m. It is the distance travelled by the car during braking. This is known as braking distance.

9. Stopping Distance = Thinking Distance + Braking Distance = 10 m + 25 m = 35 m Stopping Distance < 40 m Therefore the car will not collide with the man A.

10. Braking Force = mass x  acceleration = 500 kg x  8 m s    During braking, the slope of the v-t graph =  8 m s . This is the acceleration of the car. It points in a direction opposite to the motion of the car. Given the mass of the car is 500 kg.

11. The braking force is in fact the friction between the tyres and the road surface. When the brakes are applied, the wheels are locked and the tyres rubs against the road surface. Skid mark is left on the road surface. The braking force decreases if the road surface is wet, the surfaces of the tyres are worn out.

12. Suppose the initial velocity of the car is 40 m s -1. The reaction time of the driver remains as 0.5 s and the braking force remains as 4000 N. Will the car hit the man A with an initial separation of 40 m ? For the same braking force and same mass, the acceleration is the same. The slope of the graph remains as  8 m s  parallel

13. Suppose the initial velocity of the car is 40 m s -1. The reaction time of the driver remains as 0.5 s and the braking force remains as 4000 N. Will the car hit the man A with an initial separation of 40 m ? Stopping distance = shaded area = 120 m Stopping distance > 40 m. Therefore the car will hit the man A.

14. Suppose the reaction time of the driver is 1 s. The initial velocity remains as 20 m s -1 and the braking force remains as 4000 N. Will the car hit the man A with an initial separation of 40 m ? For the same braking force and same mass, the acceleration is the same. The slope of the graph remains as  8 m s  parallel

15. Suppose the reaction time of the driver is 1 s. The initial velocity remains as 20 m s -1 and the braking force remains as 4000 N. Will the car hit the man A with an initial separation of 40 m ? Stopping distance = shaded area = 45 m Stopping distance > 40 m. Therefore the car will hit the man A.

16. Suppose the braking force is reduced to 2000 N (e.g. due to wet surface on a rainy day). The initial velocity remains as 20 m s -1 and the reaction time of the driver remains as 0.5 s Will the car hit the man A with an initial separation of 40 m ? Braking force =  2000 N Acceleration =  2000   4 m s -2 Given the mass of the car is 500 kg. When the brakes are applied the slope of the velocity-time graph is  4 m s -2 

17. Suppose the braking force is reduced to 2000 N (e.g. due to wet surface on a rainy day). The initial velocity remains as 20 m s -1 and the reaction time of the driver remains as 0.5 s Will the car hit the man A with an initial separation of 40 m ? The slope of the graph =  4 m s 

18. Suppose the braking force is reduced to 2000 N (e.g. due to wet surface on a rainy day). The initial velocity remains as 20 m s -1 and the reaction time of the driver remains as 0.5 s Will the car hit the man A with an initial separation of 40 m ? Stopping distance = shaded area = 60 m Stopping distance > 40 m. Therefore the car will hit the man A.

19. Stopping distance depends on : the initial speed of the car, the braking force available, the mass of the car, the reaction time of the driver. On a rainy day, when the road is wet (smaller braking force available), cars should travel with lower speed and the separation of the cars should be increased. With the same braking force and initial speed, a car with larger mass requires a longer braking distance than one with smaller mass.