Relationship: Acceleration, Velocity, Force, Power, Energy, Mass

This article discusses the formula and calculation of power on a vehicle using variables: mass, speed and travel time.

It is known that a Toyota Corolla weighs 3,103 pounds (m). From the stop position (Vo), the car accelerates to a speed of 60 miles per hour (Vt) in 8 seconds (t).

  

Mass of the car, m = 3,103/2.205 = 1,407.26 kgf


Final speed, Vt = 60×1.61= 96.6 km/h


Then the acceleration is:

Initial velocity, Vo = 0 m/s

Final velocity, Vt = 96.6 km/h = 96.6×1,000/3,600 = 26.83 m/s

Acceleration, a = (Vt - Vo)/t = (26.83-0) / 8= 3.35 m/s2



Kinetic energy or work done:

E = (1/2.m.Vt.Vt) - (1/2.m.Vo.Vo) = (1/2×1,407.26×26.83×26.83) - 0 = 506,507.28 Joules


Power can be calculated by kinetic energy, which is equal to energy divided by time:

P = E/t = 506,507.28 / 8 = 63,313.41 watts = 63.31 kw


In units of horse power = 63,313.41 / 745.7 = 84.90 hp



Power can also be calculated by the force that drives the vehicle. This force is like a rope pulling a vehicle. In the image above, it is represented by a red arrow. If a measuring instrument is attached to the rope, then the force that pulls the car can be known. This force can also be determined by the following calculation.


The force that moves the car is equal to mass times acceleration:

F = m.a = 1,407.26×3.35 = 4,714.32 N


The average speed is:

V = (Vt-Vo) / 2 = (26.83-0) / 2 = 13.42 m/s

Power is calculated by force times average speed:

P = F.V = 4,720.17×13.42 = 63,344.68 watts = 63.34 kw



In this calculation, the acceleration is considered constant or average. In actual conditions, acceleration can change according to the transmission gear used. Due to the greater torque difference in low gear than in high gear. Acceleration in 1st gear will be faster than acceleration in 2nd gear. And so on, acceleration slows down in 3rd gear and higher gears.


In actual conditions, for the same acceleration as the calculation results, it takes more power than this calculation. It can reach 2-3 times bigger power. Due to efficiency and friction factors such as: road friction, transmission efficiency, engine response or throttle response, air friction (aerodynamics), and others.


In calculation, usually an error occurs when calculating the force (F). This force works to move the vehicle. So that the value is equal to mass times acceleration of the vehicle. In the image above, it can be seen as the red arrow. It's not vehicle weight or mass times gravity, which is shown in the image above as a blue arrow.


ANOTHER EXAMPLE

It is known that the Honda CBR1000RR motorcycle weighs 210 kgf with a rider weighing 80 kgf.  From the start position, it reaches a speed of 60 miles / hour with a time of 2.7 seconds.

Total mass = motorbike + rider = m = 210+80 = 290 kgf

Final speed, Vt = 60×1.61= 96.6 km/h

The acceleration is:
Initial velocity, Vo = 0 m/s
Final velocity, Vt = 96.6 km/h = 96.6×1,000/3,600 = 26.83 m/s

Acceleration, a = (Vt - Vo)/t = (26.83-0) / 2.7 = 9.94 m/s2


Kinetic energy or work done:
E = (1/2.m.Vt.Vt) - (1/2.m.Vo.Vo) = (1/2×290×26.83×26.83) - 0 = 104,378.09 Joules

Power can be calculated by kinetic energy, which is equal to energy divided by time:
P = E/t =  104,378.09  / 2.7 =  38,658.55 watts = 38.66 kw

In units of horse power = 38,658.55 / 745.7 = 51.84 hp


Power can also be calculated by the force that drives the vehicle. This force is like a rope pulling a vehicle. In the image above, it is represented by a red arrow. If a measuring instrument is attached to the rope, then the force that pulls the vehicle can be known. This force can also be determined by the following calculation.


The force that drives the motorbike is mass times acceleration:
 F = m.a = 290×9.94 = 2.882.60 N

The average speed is:
 V = (Vt-Vo) / 2 = (26.83-0) / 2 = 13.42 m/s

Power by force times average speed is:
 P = F.V = 2,882.60×13.42 = 38,684.49 watts = 38.68 kw