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Rate of Change of Acceleration Formula

GoRate of Change of Acceleration given Total Length of Valley Curve Formula

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Rate of Change of Acceleration refers to how quickly the acceleration of an object changes over time. Check FAQs

C a = \frac{v^{3}}{L s \cdot R}

C_a - Rate of Change of Acceleration?v - Design Speed?L_s - Length of Curve?R - Radius of Curve?

Rate of Change of Acceleration Example

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Here is how the Rate of Change of Acceleration equation looks like with Values.

Here is how the Rate of Change of Acceleration equation looks like with Units.

Here is how the Rate of Change of Acceleration equation looks like.

7.6313 = \frac{5^{3}}{7 \cdot 2.34}

7.6313m/s = \frac{{5m/s}^{3}}{7m \cdot 2.34m}

7.6313 = \frac{5^{3}}{7 \cdot 2.34}

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Rate of Change of Acceleration Solution

Follow our step by step solution on how to calculate Rate of Change of Acceleration?

FIRST Step Consider the formula

C a = \frac{v^{3}}{L s \cdot R}

Next Step Substitute values of Variables

∴

C a = \frac{{5m/s}^{3}}{7m \cdot 2.34m}

Next Step Prepare to Evaluate

∴

C a = \frac{5^{3}}{7 \cdot 2.34}

Next Step Evaluate

∴

C a = 7.63125763125763m/s

LAST Step Rounding Answer

∴

C a = 7.6313m/s

Rate of Change of Acceleration Formula Elements

Variables

Rate of Change of Acceleration

Rate of Change of Acceleration refers to how quickly the acceleration of an object changes over time.

Symbol: C_a

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Rate of Change of Acceleration

Design Speed

Design speed refers to the intended or planned operating speed for a particular section of a roadway or railway.

Symbol: v

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Design Speed

Length of Curve

Length of Curve is the distance along the road where the alignment changes from upward to downward slope, creating a valley-shaped concave.

Symbol: L_s

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Curve

Radius of Curve

Radius of Curve typically represents the minimum radius of the curve.

Symbol: R

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Curve

Other Formulas to find Rate of Change of Acceleration

Go Rate of Change of Acceleration given Total Length of Valley Curve

C a = {(\frac{L s}{2})}^{2} \cdot N \cdot v^{3}

Other formulas in Design of Valley Curve category

Go Length of Valley Curve given Time and Design Speed

L s = v \cdot t

Go Radius of Curve given Length of Valley Curve

R = \frac{v^{3}}{L s \cdot C a}

Go Design Speed given Length of Valley Curve

v = {(L s \cdot R \cdot C a)}^{\frac{1}{3}}

Go Time given Rate of Change of Acceleration

t = \frac{\frac{v^{2}}{R}}{C a}

How to Evaluate Rate of Change of Acceleration?

Rate of Change of Acceleration evaluator uses Rate of Change of Acceleration = (Design Speed^3)/(Length of Curve*Radius of Curve) to evaluate the Rate of Change of Acceleration, The Rate of Change of Acceleration formula is defined as the cube of the design speed and dividing it by the product of the length of the curve and the radius of the curve. Rate of Change of Acceleration is denoted by C_a symbol.

How to evaluate Rate of Change of Acceleration using this online evaluator? To use this online evaluator for Rate of Change of Acceleration, enter Design Speed (v), Length of Curve (L_s) & Radius of Curve (R) and hit the calculate button.

FAQs on Rate of Change of Acceleration

What is the formula to find Rate of Change of Acceleration?

The formula of Rate of Change of Acceleration is expressed as Rate of Change of Acceleration = (Design Speed^3)/(Length of Curve*Radius of Curve). Here is an example- 3.344034 = (5^3)/(7*2.34).

How to calculate Rate of Change of Acceleration?

With Design Speed (v), Length of Curve (L_s) & Radius of Curve (R) we can find Rate of Change of Acceleration using the formula - Rate of Change of Acceleration = (Design Speed^3)/(Length of Curve*Radius of Curve).

What are the other ways to Calculate Rate of Change of Acceleration?

Here are the different ways to Calculate Rate of Change of Acceleration-

Rate of Change of Acceleration=(Length of Curve/2)^2*Deviation Angle*Design Speed^3

Can the Rate of Change of Acceleration be negative?

No, the Rate of Change of Acceleration, measured in Speed cannot be negative.

Which unit is used to measure Rate of Change of Acceleration?

Rate of Change of Acceleration is usually measured using the Meter per Second[m/s] for Speed. Meter per Minute[m/s], Meter per Hour[m/s], Kilometer per Hour[m/s] are the few other units in which Rate of Change of Acceleration can be measured.

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Rate of Change of Acceleration Formula

​GoRate of Change of Acceleration given Total Length of Valley Curve Formula

Rate of Change of Acceleration Example

Rate of Change of Acceleration Solution

Rate of Change of Acceleration Formula Elements

Other Formulas to find Rate of Change of Acceleration

Other formulas in Design of Valley Curve category

How to Evaluate Rate of Change of Acceleration?

FAQs on Rate of Change of Acceleration

Variable Name

GoRate of Change of Acceleration given Total Length of Valley Curve Formula