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Retardation of Vehicle if Brakes are Applied to All Four Wheels Formula

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

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

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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 = g \cdot (μ brake \cdot \cos (α inclination) + \sin (α inclination))

a - Retardation of Vehicle?g - Acceleration due to Gravity?μ_brake - Coefficient of Friction for Brake?α_inclination - Angle of Inclination of plane to Horizontal?

Retardation of Vehicle if Brakes are Applied to All Four Wheels Example

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Here is how the Retardation of Vehicle if Brakes are Applied to All Four Wheels equation looks like with Values.

Here is how the Retardation of Vehicle if Brakes are Applied to All Four Wheels equation looks like with Units.

Here is how the Retardation of Vehicle if Brakes are Applied to All Four Wheels equation looks like.

9.0177 = 9.8 \cdot (0.92 \cdot \cos (0.01) + \sin (0.01))

9.0177m/s² = 9.8m/s² \cdot (0.92 \cdot \cos (0.01°) + \sin (0.01°))

9.0177 = 9.8 \cdot (0.92 \cdot \cos (0.01) + \sin (0.01))

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Retardation of Vehicle if Brakes are Applied to All Four Wheels Solution

Follow our step by step solution on how to calculate Retardation of Vehicle if Brakes are Applied to All Four Wheels?

FIRST Step Consider the formula

a = g \cdot (μ brake \cdot \cos (α inclination) + \sin (α inclination))

Next Step Substitute values of Variables

∴

a = 9.8m/s² \cdot (0.92 \cdot \cos (0.01°) + \sin (0.01°))

Next Step Convert Units

∴

a = 9.8m/s² \cdot (0.92 \cdot \cos (0.0002rad) + \sin (0.0002rad))

Next Step Prepare to Evaluate

∴

a = 9.8 \cdot (0.92 \cdot \cos (0.0002) + \sin (0.0002))

Next Step Evaluate

∴

a = 9.01771028533674m/s²

LAST Step Rounding Answer

∴

a = 9.0177m/s²

Retardation of Vehicle if Brakes are Applied to All Four Wheels 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 Vehicle

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 Gravity

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: μ_brake

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Coefficient of Friction for Brake

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: α_inclination

Measurement: AngleUnit: °

Note: Value should be between 0 to 90.

Formulas to find Angle of Inclination of plane to Horizontal

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 \cdot (μ brake \cdot \cos (α inclination) - \sin (α inclination))

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

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

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

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

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

a = g \cdot μ brake

How to Evaluate Retardation of Vehicle if Brakes are Applied to All Four Wheels?

Retardation of Vehicle if Brakes are Applied to All Four Wheels evaluator uses 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)) to evaluate the Retardation of Vehicle, Retardation of Vehicle if Brakes are Applied to All Four Wheels formula is defined as the deceleration of a vehicle when all four wheels are braked, taking into account the brake's frictional force, the vehicle's inclination, and gravity, providing a measure of the vehicle's ability to come to a stop safely and efficiently. Retardation of Vehicle is denoted by a symbol.

How to evaluate Retardation of Vehicle if Brakes are Applied to All Four Wheels using this online evaluator? To use this online evaluator for Retardation of Vehicle if Brakes are Applied to All Four Wheels, enter Acceleration due to Gravity (g), Coefficient of Friction for Brake (μ_brake) & Angle of Inclination of plane to Horizontal (α_inclination) and hit the calculate button.

FAQs on Retardation of Vehicle if Brakes are Applied to All Four Wheels

What is the formula to find Retardation of Vehicle if Brakes are Applied to All Four Wheels?

The formula of Retardation of Vehicle if Brakes are Applied to All Four Wheels is expressed as 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)). Here is an example- 8.91971 = 9.8*(0.92*cos(0.0001745329251994)+sin(0.0001745329251994)).

How to calculate Retardation of Vehicle if Brakes are Applied to All Four Wheels?

With Acceleration due to Gravity (g), Coefficient of Friction for Brake (μ_brake) & Angle of Inclination of plane to Horizontal (α_inclination) we can find Retardation of Vehicle if Brakes are Applied to All Four Wheels using the formula - 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)). This formula also uses Sine (sin), Cosine (cos) 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))
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)

Can the Retardation of Vehicle if Brakes are Applied to All Four Wheels be negative?

Yes, the Retardation of Vehicle if Brakes are Applied to All Four Wheels, measured in Acceleration can be negative.

Which unit is used to measure Retardation of Vehicle if Brakes are Applied to All Four Wheels?

Retardation of Vehicle if Brakes are Applied to All Four Wheels 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 Brakes are Applied to All Four Wheels can be measured.

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