Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only 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%
✖Angle of Inclination of plane to Horizontal is the angle at which a plane is tilted from the horizontal surface, affecting the retardation of a vehicle.ⓘ Angle of Inclination of plane to Horizontal [α_inclination]			+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 if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only [a]

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Formula

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

Formula

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

Example

9.000079 m/s² = \frac{0.92 \cdot 9.8 m/s² \cdot \cos (0.01 °) \cdot (360 m - 0.2 m)}{360 m + 0.92 \cdot 0.4 m} - 9.8 m/s² \cdot \sin (0.01 °)

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

STEP 0: Pre-Calculation Summary

Formula Used

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)
a = (μ_brake*g*cos(α_inclination)*(L-x))/(L+μ_brake*h)-g*sin(α_inclination)
This formula uses 2 Functions, 7 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

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.
Angle of Inclination of plane to Horizontal - (Measured in Radian) - Angle of Inclination of plane to Horizontal is the angle at which a plane is tilted from the horizontal surface, affecting the retardation of a 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
Angle of Inclination of plane to Horizontal: 0.01 Degree --> 0.0001745329251994 Radian (Check conversion here)
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*cos(α_inclination)*(L-x))/(L+μ_brake*h)-g*sin(α_inclination) --> (0.92*9.8*cos(0.0001745329251994)*(360-0.2))/(360+0.92*0.4)-9.8*sin(0.0001745329251994)

Evaluating ... ...

a = 9.00007872230386

STEP 3: Convert Result to Output's Unit

9.00007872230386 Meter per Square Second --> No Conversion Required

FINAL ANSWER

9.00007872230386 ≈ 9.000079 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 if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only

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

What is Braking System in a Vehicle?

A braking system in a vehicle is responsible for slowing down or stopping the vehicle by applying friction to its wheels. It typically consists of components like brake pads, discs, or drums, and operates through hydraulic, mechanical, or electronic means. The system ensures controlled deceleration for safety during driving.

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

Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only calculator uses 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) to calculate the Retardation of Vehicle, Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only formula is defined as the deceleration of a vehicle moving down a plane when brakes are applied to the rear wheels, taking into account the brake friction, gravity, and the inclination of the plane. Retardation of Vehicle is denoted by a symbol.

How to calculate Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only using this online calculator? To use this online calculator for Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only, enter Coefficient of Friction for Brake (μ_brake), Acceleration due to Gravity (g), Angle of Inclination of plane to Horizontal (α_inclination), 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 if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only calculation can be explained with given input values -> 8.977562 = (0.92*9.8*cos(0.0001745329251994)*(360-0.2))/(360+0.92*0.4)-9.8*sin(0.0001745329251994).

FAQ

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

Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only formula is defined as the deceleration of a vehicle moving down a plane when brakes are applied to the rear wheels, taking into account the brake friction, gravity, and the inclination of the plane and is represented as a = (μ_brake*g*cos(α_inclination)*(L-x))/(L+μ_brake*h)-g*sin(α_inclination) or 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). 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, Angle of Inclination of plane to Horizontal is the angle at which a plane is tilted from the horizontal surface, affecting the retardation of a 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 if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only?

Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only formula is defined as the deceleration of a vehicle moving down a plane when brakes are applied to the rear wheels, taking into account the brake friction, gravity, and the inclination of the plane is calculated using 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). To calculate Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only, you need Coefficient of Friction for Brake (μ_brake), Acceleration due to Gravity (g), Angle of Inclination of plane to Horizontal (α_inclination), 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, Angle of Inclination of plane to Horizontal, 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, Angle of Inclination of plane to Horizontal, 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 = Acceleration due to Gravity*Coefficient of Friction for Brake

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