# Car Acceleration

## Calculate acceleration of car

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**

s*tart speed (km/h)*

*final speed (km/h)*

*time used (s)*

*mass of object (kg)*

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

#### mph

*start speed (mph)*

*final speed (mph)*

*time used (s)*

### Car Acceleration Diagram - *km/h*

### 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 of some known cars

### 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