# Calculating the Stopping distance

• xavierengineering
In summary: Oops, of course, you're right. My only defense is that the engineer in me is more comfortable going the "F=ma" route.
xavierengineering

## Homework Statement

A car of mass 1000 kg is cruising at 120 km/hr. At this velocity the drag and friction forces that the engine needs to work against is equivalent to 450 N.

(i) What is the propulsive power being delivered by the engine when cruising? (4 marks)

(ii) From a velocity of 100 km/hr, the driver suddenly sees a traffic jam ahead and performs an emergency braking, resulting in locking the four wheels. Calculate the minimum braking distance required to bring the car to a full stop.

Assume the following: The coefficient of friction between the tyres and road is μ = 0.8.
Consider the weight of the vehicle to be equally distributed on each wheel while braking The drag or other friction forces are not significant in this case. g = 9.8 m/s2

D=V/2*0.8*9.81

## The Attempt at a Solution

All i know for the equation is D=V/2*0.8*9.81. However i am not sure how to implement the mass into the equation, Or if there is a different one to use.

Last edited by a moderator:
The equation you quote is fine for part two. Why do you wish to bring mass into it?
For part one, you need some more standard equations. What ones do you know about power, force, mass, acceleration?

I worked out Q 1 = 15KW
By using the P= 450*(120/3.6)=15KW

But for part be i assumed the weight must be added to the equation because it states the mass of the car. Or is that figure irrelevant to work out the distance ?

I also forgot to add this to the question..
The driver cannot avoid hitting the vehicle at the back of the queue. At the moment of impact, the driver's car has a remaining velocity of 15 km/hr and hits a stationary van that has a mass 1400 kg.
Assume that both vehicles are in neutral and not braking at the moment of impact. Neglect the effects of friction.

Calculate the velocities of each vehicle after impact if the coefficient of restitution of the vehicles' bumpers is 0.85.

xavierengineering said:
I also forgot to add this to the question..
The driver cannot avoid hitting the vehicle at the back of the queue. At the moment of impact, the driver's car has a remaining velocity of 15 km/hr and hits a stationary van that has a mass 1400 kg.
Assume that both vehicles are in neutral and not braking at the moment of impact. Neglect the effects of friction.

Calculate the velocities of each vehicle after impact if the coefficient of restitution of the vehicles' bumpers is 0.85.
That's the part where you need the mass of the car.

xavierengineering
I believe you need the mass of the car to get the drag force on it while skidding to a stop.

insightful said:
I believe you need the mass of the car to get the drag force on it while skidding to a stop.
No. We are given g, the coefficient of friction, and the initial and final speeds, and we wish to find a distance. None of those involves a mass dimension. Consequently (by dimensional analysis) being told one mass as well cannot be of use.

haruspex said:
No. We are given g, the coefficient of friction, and the initial and final speeds, and we wish to find a distance. None of those involves a mass dimension. Consequently (by dimensional analysis) being told one mass as well cannot be of use.
Oops, of course, you're right. My only defense is that the engineer in me is more comfortable going the "F=ma" route.

## 1. What is the formula for calculating stopping distance?

The formula for calculating stopping distance is stopping distance = thinking distance + braking distance. This means that the total stopping distance is equal to the distance traveled during the driver's reaction time plus the distance traveled while braking.

## 2. How is thinking distance calculated?

Thinking distance is calculated by multiplying the vehicle's initial speed by the time it takes the driver to react. The average reaction time for a driver is 0.75 seconds, so the formula for thinking distance is thinking distance = initial speed x 0.75.

## 3. How is braking distance calculated?

Braking distance is calculated by taking into account the vehicle's deceleration, which is affected by factors such as the condition of the brakes and the road surface. The formula for braking distance is braking distance = (initial speed x stopping distance) / (2 x deceleration).

## 4. What factors can affect stopping distance?

Stopping distance can be affected by several factors, including the initial speed of the vehicle, the condition and type of brakes, the road surface and weather conditions, the weight and condition of the vehicle, and the driver's reaction time and braking skills.

## 5. How can I reduce my vehicle's stopping distance?

To reduce your vehicle's stopping distance, you can maintain a safe speed, ensure that your brakes are in good condition, and keep a safe distance from the vehicle in front of you. It is also important to stay alert and focused while driving to reduce your reaction time. Additionally, regularly maintaining your vehicle and checking tire pressure can also help improve braking performance.

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