Retardation of Vehicle when Vehicle Moves on Level Track if Brakes are Applied to Rear Wheels Calculator

✖Coefficient of Friction for Brake Retardation is a measure of the frictional force that opposes the motion of a vehicle, slowing it down during braking.ⓘ Coefficient of Friction for Brake [μ_brake]			+10% -10%
✖Acceleration due to Gravity is the rate at which the velocity of an object decreases as it moves under the influence of gravity, slowing down the vehicle.ⓘ Acceleration due to Gravity [g]			+10% -10%
✖Distance between Center of Rear and Front Wheels is the length between the center of the rear wheel and the center of the front wheel of a vehicle.ⓘ Distance between Center of Rear and Front Wheels [L]			+10% -10%
✖Perpendicular distance of C.G is the shortest distance from the centre of gravity of a vehicle to the point where it is pivoted during retardation.ⓘ Perpendicular Distance of C.G [x]			+10% -10%
✖Height of C.G. of Vehicle is the vertical distance of the center of gravity from the ground level of a vehicle, affecting its stability and balance.ⓘ Height of C.G. of Vehicle [h]			+10% -10%

✖Retardation of vehicle is the rate of decrease of velocity of a vehicle with respect to time, usually measured in meters per second squared.ⓘ Retardation of Vehicle when Vehicle Moves on Level Track if Brakes are Applied to Rear Wheels [a]

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Formula

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Retardation of Vehicle when Vehicle Moves on Level Track if Brakes are Applied to Rear Wheels

Formula

a = \frac{μ brake \cdot g \cdot (L - x)}{L + μ brake \cdot h}

Example

9.001789 m/s² = \frac{0.92 \cdot 9.8 m/s² \cdot (360 m - 0.2 m)}{360 m + 0.92 \cdot 0.4 m}

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Retardation of Vehicle when Vehicle Moves on Level Track if Brakes are Applied to Rear Wheels Solution

STEP 0: Pre-Calculation Summary

Formula Used

Retardation of Vehicle = (Coefficient of Friction for Brake*Acceleration due to Gravity*(Distance between Center of Rear and Front Wheels-Perpendicular Distance of C.G))/(Distance between Center of Rear and Front Wheels+Coefficient of Friction for Brake*Height of C.G. of Vehicle)
a = (μ_brake*g*(L-x))/(L+μ_brake*h)
This formula uses 6 Variables

Variables Used

Retardation of Vehicle - (Measured in Meter per Square Second) - Retardation of vehicle is the rate of decrease of velocity of a vehicle with respect to time, usually measured in meters per second squared.
Coefficient of Friction for Brake - Coefficient of Friction for Brake Retardation is a measure of the frictional force that opposes the motion of a vehicle, slowing it down during braking.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration due to Gravity is the rate at which the velocity of an object decreases as it moves under the influence of gravity, slowing down the vehicle.
Distance between Center of Rear and Front Wheels - (Measured in Meter) - Distance between Center of Rear and Front Wheels is the length between the center of the rear wheel and the center of the front wheel of a vehicle.
Perpendicular Distance of C.G - (Measured in Meter) - Perpendicular distance of C.G is the shortest distance from the centre of gravity of a vehicle to the point where it is pivoted during retardation.
Height of C.G. of Vehicle - (Measured in Meter) - Height of C.G. of Vehicle is the vertical distance of the center of gravity from the ground level of a vehicle, affecting its stability and balance.

STEP 1: Convert Input(s) to Base Unit

Coefficient of Friction for Brake: 0.92 --> No Conversion Required
Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required
Distance between Center of Rear and Front Wheels: 360 Meter --> 360 Meter No Conversion Required
Perpendicular Distance of C.G: 0.2 Meter --> 0.2 Meter No Conversion Required
Height of C.G. of Vehicle: 0.4 Meter --> 0.4 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a = (μ_brake*g*(L-x))/(L+μ_brake*h) --> (0.92*9.8*(360-0.2))/(360+0.92*0.4)

Evaluating ... ...

a = 9.00178928206722

STEP 3: Convert Result to Output's Unit

9.00178928206722 Meter per Square Second --> No Conversion Required

FINAL ANSWER

9.00178928206722 ≈ 9.001789 Meter per Square Second <-- Retardation of Vehicle

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Brakes and Dynamometers » Mechanical » Retardation of the Vehicle » Retardation of Vehicle when Vehicle Moves on Level Track if Brakes are Applied to Rear Wheels

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Indian Institute of Information Technology (IIIT), Guwahati

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< Retardation of the Vehicle Calculators

Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only

Go Retardation of Vehicle = (Coefficient of Friction for Brake*Acceleration due to Gravity*cos(Angle of Inclination of plane to Horizontal)*(Distance between Center of Rear and Front Wheels-Perpendicular Distance of C.G))/(Distance between Center of Rear and Front Wheels+Coefficient of Friction for Brake*Height of C.G. of Vehicle)-Acceleration due to Gravity*sin(Angle of Inclination of plane to Horizontal)

Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to Front Wheels only

Go Retardation of Vehicle = (Coefficient of Friction for Brake*Acceleration due to Gravity*cos(Angle of Inclination of plane to Horizontal)*Perpendicular Distance of C.G)/(Distance between Center of Rear and Front Wheels-Coefficient of Friction for Brake*Height of C.G. of Vehicle)-Acceleration due to Gravity*sin(Angle of Inclination)

Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to All Four Wheels

Go Retardation of Vehicle = Acceleration due to Gravity*(Coefficient of Friction for Brake*cos(Angle of Inclination of plane to Horizontal)-sin(Angle of Inclination of plane to Horizontal))

Retardation of Vehicle when Vehicle Moves on Level Track if Brakes are Applied to All Four Wheels

Go Retardation of Vehicle = Acceleration due to Gravity*Coefficient of Friction for Brake

Retardation of Vehicle when Vehicle Moves on Level Track if Brakes are Applied to Rear Wheels Formula

What is Opposing Force in Vehicle?

Opposing forces in a vehicle are forces that resist its motion, such as air resistance (drag), friction between the tires and the road, and mechanical resistance in components like the drivetrain. These forces act against the vehicle’s movement, slowing it down or requiring more energy to maintain speed.

How to Calculate Retardation of Vehicle when Vehicle Moves on Level Track if Brakes are Applied to Rear Wheels?

Retardation of Vehicle when Vehicle Moves on Level Track if Brakes are Applied to Rear Wheels calculator uses Retardation of Vehicle = (Coefficient of Friction for Brake*Acceleration due to Gravity*(Distance between Center of Rear and Front Wheels-Perpendicular Distance of C.G))/(Distance between Center of Rear and Front Wheels+Coefficient of Friction for Brake*Height of C.G. of Vehicle) to calculate the Retardation of Vehicle, Retardation of Vehicle when Vehicle Moves on Level Track if Brakes are Applied to Rear Wheels formula is defined as the deceleration of a vehicle when brakes are applied to the rear wheels on a level track, taking into account the brake friction, gravity, and the vehicle's dimensions, to determine the rate of slowing down. Retardation of Vehicle is denoted by a symbol.

How to calculate Retardation of Vehicle when Vehicle Moves on Level Track if Brakes are Applied to Rear Wheels using this online calculator? To use this online calculator for Retardation of Vehicle when Vehicle Moves on Level Track if Brakes are Applied to Rear Wheels, enter Coefficient of Friction for Brake (μ_brake), Acceleration due to Gravity (g), Distance between Center of Rear and Front Wheels (L), Perpendicular Distance of C.G (x) & Height of C.G. of Vehicle (h) and hit the calculate button. Here is how the Retardation of Vehicle when Vehicle Moves on Level Track if Brakes are Applied to Rear Wheels calculation can be explained with given input values -> 8.979272 = (0.92*9.8*(360-0.2))/(360+0.92*0.4).

FAQ

What is Retardation of Vehicle when Vehicle Moves on Level Track if Brakes are Applied to Rear Wheels?

Retardation of Vehicle when Vehicle Moves on Level Track if Brakes are Applied to Rear Wheels formula is defined as the deceleration of a vehicle when brakes are applied to the rear wheels on a level track, taking into account the brake friction, gravity, and the vehicle's dimensions, to determine the rate of slowing down and is represented as a = (μ_brake*g*(L-x))/(L+μ_brake*h) or Retardation of Vehicle = (Coefficient of Friction for Brake*Acceleration due to Gravity*(Distance between Center of Rear and Front Wheels-Perpendicular Distance of C.G))/(Distance between Center of Rear and Front Wheels+Coefficient of Friction for Brake*Height of C.G. of Vehicle). Coefficient of Friction for Brake Retardation is a measure of the frictional force that opposes the motion of a vehicle, slowing it down during braking, Acceleration due to Gravity is the rate at which the velocity of an object decreases as it moves under the influence of gravity, slowing down the vehicle, Distance between Center of Rear and Front Wheels is the length between the center of the rear wheel and the center of the front wheel of a vehicle, Perpendicular distance of C.G is the shortest distance from the centre of gravity of a vehicle to the point where it is pivoted during retardation & Height of C.G. of Vehicle is the vertical distance of the center of gravity from the ground level of a vehicle, affecting its stability and balance.

How to calculate Retardation of Vehicle when Vehicle Moves on Level Track if Brakes are Applied to Rear Wheels?

Retardation of Vehicle when Vehicle Moves on Level Track if Brakes are Applied to Rear Wheels formula is defined as the deceleration of a vehicle when brakes are applied to the rear wheels on a level track, taking into account the brake friction, gravity, and the vehicle's dimensions, to determine the rate of slowing down is calculated using Retardation of Vehicle = (Coefficient of Friction for Brake*Acceleration due to Gravity*(Distance between Center of Rear and Front Wheels-Perpendicular Distance of C.G))/(Distance between Center of Rear and Front Wheels+Coefficient of Friction for Brake*Height of C.G. of Vehicle). To calculate Retardation of Vehicle when Vehicle Moves on Level Track if Brakes are Applied to Rear Wheels, you need Coefficient of Friction for Brake (μ_brake), Acceleration due to Gravity (g), Distance between Center of Rear and Front Wheels (L), Perpendicular Distance of C.G (x) & Height of C.G. of Vehicle (h). With our tool, you need to enter the respective value for Coefficient of Friction for Brake, Acceleration due to Gravity, Distance between Center of Rear and Front Wheels, Perpendicular Distance of C.G & Height of C.G. of Vehicle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Retardation of Vehicle?

In this formula, Retardation of Vehicle uses Coefficient of Friction for Brake, Acceleration due to Gravity, Distance between Center of Rear and Front Wheels, Perpendicular Distance of C.G & Height of C.G. of Vehicle. We can use 3 other way(s) to calculate the same, which is/are as follows -

Retardation of Vehicle = Acceleration due to Gravity*(Coefficient of Friction for Brake*cos(Angle of Inclination of plane to Horizontal)-sin(Angle of Inclination of plane to Horizontal))
Retardation of Vehicle = (Coefficient of Friction for Brake*Acceleration due to Gravity*cos(Angle of Inclination of plane to Horizontal)*Perpendicular Distance of C.G)/(Distance between Center of Rear and Front Wheels-Coefficient of Friction for Brake*Height of C.G. of Vehicle)-Acceleration due to Gravity*sin(Angle of Inclination)
Retardation of Vehicle = (Coefficient of Friction for Brake*Acceleration due to Gravity*cos(Angle of Inclination of plane to Horizontal)*(Distance between Center of Rear and Front Wheels-Perpendicular Distance of C.G))/(Distance between Center of Rear and Front Wheels+Coefficient of Friction for Brake*Height of C.G. of Vehicle)-Acceleration due to Gravity*sin(Angle of Inclination of plane to Horizontal)

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