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# Car Acceleration

If you know the initial and final velocity of a car (or whatever) - and the time used - the average acceleration can be calculated as

a = dv / dt

= (v f - v s ) / dt                                           (1)

where

a = acceleration of object (m/s 2 , ft/s 2 )

dv = change in velocity (m/s, ft/s)

v f = final speed (m/s, ft/s)

v s = start speed (m/s, ft/s)

dt = time used (s)

Common benchmark velocities for acceleration of cars and motorcycles are

• 0 - 60 mph = 0 - 26.8 m/s = 0 - 96.6 km/h
• 0 - 100 km/h = 0 - 27.8 m/s = 0 - 62.1 mph

### Online Car Acceleration Calculator

km/h

Note that force, work and power are calculated for mass acceleration only. Forces due to air resistance ( drag ) and rolling friction are not included.

### Car Acceleration Diagram - mph

If you know the distance moved and the time used - the acceleration can be calculated as

a = 2 ds / dt 2 (2)

where

ds = distance moved (m, ft)

### Acceleration Force

The acceleration force can be calculated as

F = m a                                (3)

where

F = acceleration force (N, lb f )

m = mass of car (kg, slugs)

### Acceleration Work

The acceleration work can be calculated as

W = F l                                    (4)

where

W = work done (Nm, J, ft lb f )

l = distance moved (m, ft)

### Acceleration Power

The acceleration power can be calculated as

P = W / dt                                  (5)

where

P = power (J/s, W, ft lb f /s)

### Example - Car Acceleration

A car with mass 1000 kg (2205 lb m ) accelerates from 0 m/s (0 ft/s) to 27.8 m/s (100 km/h, 91.1 ft/s, 62.1 mph) in 10 s .

The acceleration can be calculated from eq. 1 as

a = ((27.8 m/s) - (0 m/s)) / (10 s)

= 2.78 m/s 2

The acceleration force can be calculated from eq. 3 as

F = (1000 kg) (2.78 m/s 2 )

= 2780 N

The distance moved can be calculated by rearranging eq. 2 to

ds = a dt 2 / 2

= (2.78 m/s 2 ) (10 s) 2 / 2

= 139 m

The acceleration work can be calculated from eq. 4 as

W = (2780 N) (139 m)

= 386420 J

The acceleration power can be calculated from eq. 5 as

P = (386420 J) / (10 s)

= 38642 W

= 38.6 kW

The calculation can also be done in Imperial units :

The acceleration can be calculated from eq. 1 as

a = ((91.1 ft/s) - (0 ft/s)) / (10 s)

= 9.11 ft/s 2

In the Imperial system mass is measured in slugs where 1 slug = 32.17405 lb m

The acceleration force can be calculated from eq. 3 as

F = (( 2205 lb m ) (1/32.17405 (slugs/ lb m )) ) (9.11 ft/s 2 )

= 624 lb f

The distance moved can be calculated by rearranging eq. 2 to

ds = a dt 2 / 2

= (9.11 ft/s 2 ) (10 s) 2 / 2

= 455 ft

The acceleration work can be calculated from eq. 4 as

W = (624 lb f ) (455 ft)

= 284075 ft lb f

• 1 ft lb f = 1.36 J

The acceleration power can be calculated from eq. 5 as

P = (284075 ft lb f ) / (10 s)

= 28407 ft lb f /s

• 1 ft lb f /s = 1.36 W = 0.00182 hp

## Related Topics

### • Dynamics

Motion - velocity and acceleration, forces and torque.

### • Mechanics

Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.

## Related Documents

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Change in velocity vs. time used.

### Acceleration of Gravity and Newton's Second Law

Acceleration of gravity and Newton's Second Law - SI and Imperial units.

### Acceleration Units Converter

Converting between units of acceleration.

### Acceleration vs. Velocity Equations

Useful equations related to acceleration, average velocity, final velocity and distance traveled.

### Car - Required Power and Torque

Power, torque, efficiency and wheel force acting on a car.

### Car - Traction Force

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### Car Fuel Consumption - liter/100 km

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### Cars - New vs. Old Car Cost Calculator

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### Centripetal and Centrifugal Acceleration Force

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### Disk Brakes - Torque and Force

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### Driving Distances between European Cities

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### Electrical Vehicle Charging - Power vs. Voltage and Amps

EV Charging - AC vs. DC, single phase vs. three phase and power vs. voltage and amps.

### Formulas of Motion - Linear and Circular

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### Fuel Consumption - mpg

Calculate fuel consumption in miles per gallon - mpg - calculator and consumption charts.

### Impact Force

Impact forces acting on falling objects hitting the ground, cars crashing and similar cases.

### Kinetic Energy

Energy possessed by an object's motion is kinetic energy.

### Piston Engines - Compression Ratios

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### Piston Engines - Displacement

Calculate piston engine displacement.

### Rolling Resistance

Rolling friction and rolling resistance.

### Toggle Joint

A toggle joint mechanism can be used to multiply force.

### Vehicle - Distance Traveled vs. Velcocity and Time Used (mph)

Speed (mph) and time (hours) and distance traveled (miles) chart.

### Vehicle - Distance Traveled vs. Velocity and Time (km/h)

Speed (km/h) vs. time (hours) and distance traveled (km).

### Vehicles Traffic Flow and Density

Traffic flow and density as used in highway design.

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