Braking Distances
Kinetic Energy. Braking distance increases four times each time the starting speed doubles. This is because the work done in bringing a car to rest means removing all of its kinetic energy.
Work done = kinetic energy.
Work done = braking force x distance.
W = F x d.
Kinetic Energy = 1\\2 X mass X velocity2.
This means that:
F x d = 1/2 x m x v2
Therefore, for a fixed maximum braking force, the braking distance is proportional to the square of the velocity.
Question.
Calculate the total breaking distance of a car travelling at 12m/s, when the driver’s reaction time is 0.5s and they see a child run into the road?
Additional Information:
Car Mass: 900Kg.
Braking Force: 2000N.
Calculations:
Part 1. Reaction (Thinking) Distance:
Distance = speed x time.
d = v x t.
Therefore, d = 12m/s x 0.5s
Thinking Distance = 6m.
Part 2. Braking distance calculation:
F x d = 1/2 x m x v2
Transposed:
d = (m x v2)/f x (1/2)
d = (900 x 122)/2000 x (1/2)
Braking Distance = 32 metres.
Therefore, the total stopping distance is:
Stopping distance = Reaction distance + Braking distance.
Stopping distance = 6 + 32.
Answer: 38m
Braking Distances
Kinetic Energy. Braking distance increases four times each time the starting speed doubles. This is because the work done in bringing a car to rest means removing all of its kinetic energy.
Work done = kinetic energy.
Work done = braking force x distance.
W = F x d.
Kinetic Energy = 1\\2 X mass X velocity2.
This means that:
F x d = 1/2 x m x v2
Therefore, for a fixed maximum braking force, the braking distance is proportional to the square of the velocity.
Question.
Calculate the total breaking distance of a car travelling at 12m/s, when the driver’s reaction time is 0.5s and they see a child run into the road?
Additional Information:
Car Mass: 900Kg.
Braking Force: 2000N.
Calculations:
Part 1. Reaction (Thinking) Distance:
Distance = speed x time.
d = v x t.
Therefore, d = 12m/s x 0.5s
Thinking Distance = 6m.
Part 2. Braking distance calculation:
F x d = 1/2 x m x v2
Transposed:
d = (m x v2)/f x (1/2)
d = (900 x 122)/2000 x (1/2)
Braking Distance = 32 metres.
Therefore, the total stopping distance is:
Stopping distance = Reaction distance + Braking distance.
Stopping distance = 6 + 32.
Answer: 38m
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