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Braking distance question. 10 points?
Braking force = 70% weight of a car (in this particular car)
Show that the braking distance of the car in metres, initially travelling at speed v is:
Braking distance is approx 0.073v²
Anyone got any help or tips? Or maybe a place to start like a formula or something?
2 Answers
- DaveWHLv 710 years agoFavorite Answer
From the equations of motion we have
u^2 = v^2 + 2ax
where u = final velocity; v = initial velocity; a = acceleration; x = distance travelled
Here, we are looking for a negative acceleration so
u^2 = v^2 - 2 ax
But u = 0
v^2 = - 2ax
We are told that the breaking force is 70% of the weight of the car. So
F(b) = mass * decelleration = 0.7 mg
- a = 0.7g
substituting this value of a in the above equation we get
v^2 = 2 * 0.7g x
x = v^2 / (2 * 0.7 * 9.8) = 0.073 v^2
- AmyLv 710 years ago
From the force, calculate the acceleration (mass will cancel out).
The acceleration doesn't depend on speed, so you can use the equations of motion under constant acceleration. Assume an initial speed of v and final speed of 0.
(as an intermediate step, you may want to calculate the time it takes to brake)
