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Retardation of vehicle is the rate of decrease of velocity of a vehicle with respect to time, usually measured in meters per second squared. Check FAQs
a=μbrake⋅g⋅cos(αinclination)⋅(L-x)L+μbrake⋅h-g⋅sin(αinclination)
a - Retardation of Vehicle?μbrake - Coefficient of Friction for Brake?g - Acceleration due to Gravity?αinclination - Angle of Inclination of plane to Horizontal?L - Distance between Center of Rear and Front Wheels?x - Perpendicular Distance of C.G?h - Height of C.G. of Vehicle?

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

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Here is how the Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only equation looks like with Values.

Here is how the Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only equation looks like with Units.

Here is how the Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only equation looks like.

9.0001Edit=0.92Edit⋅9.8Edit⋅cos(0.01Edit)⋅(360Edit-0.2Edit)360Edit+0.92Edit⋅0.4Edit-9.8Edit⋅sin(0.01Edit)
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Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only Solution

Follow our step by step solution on how to calculate Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only?

FIRST Step Consider the formula
a=μbrake⋅g⋅cos(αinclination)⋅(L-x)L+μbrake⋅h-g⋅sin(αinclination)
Next Step Substitute values of Variables
∴ a=0.92⋅9.8m/s²⋅cos(0.01°)⋅(360m-0.2m)360m+0.92⋅0.4m-9.8m/s²⋅sin(0.01°)
Next Step Convert Units
∴ a=0.92⋅9.8m/s²⋅cos(0.0002rad)⋅(360m-0.2m)360m+0.92⋅0.4m-9.8m/s²⋅sin(0.0002rad)
Next Step Prepare to Evaluate
∴ a=0.92⋅9.8⋅cos(0.0002)⋅(360-0.2)360+0.92⋅0.4-9.8⋅sin(0.0002)
Next Step Evaluate
∴a=9.00007872230386m/s²
LAST Step Rounding Answer
∴a=9.0001m/s²

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

Variables
Functions
Retardation of Vehicle
Retardation of vehicle is the rate of decrease of velocity of a vehicle with respect to time, usually measured in meters per second squared.
Symbol: a
Measurement: AccelerationUnit: m/s²
Note: Value can be positive or negative.
Formulas to find Retardation of VehicleOpen Variable
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.
Symbol: μbrake
Measurement: NAUnit: Unitless
Note: Value should be between 0 to 1.
Formulas to find Coefficient of Friction for BrakeOpen Variable
Acceleration due to Gravity
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.
Symbol: g
Measurement: AccelerationUnit: m/s²
Note: Value should be greater than 0.
Formulas to find Acceleration due to GravityOpen Variable
Angle of Inclination of plane to Horizontal
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.
Symbol: αinclination
Measurement: AngleUnit: °
Note: Value should be between 0 to 90.
Formulas to find Angle of Inclination of plane to HorizontalOpen Variable
Distance between Center of Rear and Front Wheels
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.
Symbol: L
Measurement: LengthUnit: m
Note: Value should be greater than 0.
Formulas to find Distance between Center of Rear and Front WheelsOpen Variable
Perpendicular Distance of C.G
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.
Symbol: x
Measurement: LengthUnit: m
Note: Value should be greater than 0.
Formulas to find Perpendicular Distance of C.GOpen Variable
Height of C.G. of Vehicle
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.
Symbol: h
Measurement: LengthUnit: m
Note: Value should be greater than 0.
Formulas to find Height of C.G. of VehicleOpen Variable
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.
Syntax: sin(Angle)
cos
Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.
Syntax: cos(Angle)

Other Formulas to find Retardation of Vehicle

​Go Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to All Four Wheels
a=g⋅(μbrake⋅cos(αinclination)-sin(αinclination))
​Go Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to Front Wheels only
a=μbrake⋅g⋅cos(αinclination)⋅xL-μbrake⋅h-g⋅sin(θi)

How to Evaluate 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 evaluator 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 evaluate 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 evaluate Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only using this online evaluator? To use this online evaluator for Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only, enter Coefficient of Friction for Brake (μbrake), Acceleration due to Gravity (g), Angle of Inclination of plane to Horizontal (αinclination), 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.

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

What is the formula to find Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only?
The formula of Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only is expressed as 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). Here is an example- 8.977562 = (0.92*9.8*cos(0.0001745329251994)*(360-0.2))/(360+0.92*0.4)-9.8*sin(0.0001745329251994).
How to calculate Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only?
With Coefficient of Friction for Brake (μbrake), Acceleration due to Gravity (g), Angle of Inclination of plane to Horizontal (αinclination), Distance between Center of Rear and Front Wheels (L), Perpendicular Distance of C.G (x) & Height of C.G. of Vehicle (h) we can find Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only using the formula - 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). This formula also uses Sine, Cosine function(s).
What are the other ways to Calculate Retardation of Vehicle?
Here are the different ways to Calculate Retardation of Vehicle-
  • 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))OpenImg
  • 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)OpenImg
  • Retardation of Vehicle=Acceleration due to Gravity*Coefficient of Friction for BrakeOpenImg
Can the Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only be negative?
Yes, the Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only, measured in Acceleration can be negative.
Which unit is used to measure 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 is usually measured using the Meter per Square Second[m/s²] for Acceleration. Kilometer per Square Second[m/s²], Micrometer per Square Second[m/s²], Mile per Square Second[m/s²] are the few other units in which Retardation of Vehicle if Vehicle Moves down Plane if Brakes are Applied to Rear Wheels only can be measured.
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