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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

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

where

a = acceleration of object (m/s2, ft/s2)

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

vf = 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, lbf )

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 lbf )

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 lbf /s)

Example - Car Acceleration

A car with mass 1000 kg (2205 lbm ) 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 average acceleration can be calculated from eq. 1 as

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

= 2.78 m/s2

The average acceleration force can be calculated from eq. 3 as

F = (1000 kg) (2.78 m/s2)

= 2780 N

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

ds = a dt2/ 2

= (2.78 m/s2) (10 s)2/ 2

= 139 m

The average acceleration work can be calculated from eq. 4 as

W = (2780 N) (139 m)

= 386420 J

The average 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 average acceleration can be calculated from eq. 1 as

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

= 9.11 ft/s2

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

The average acceleration force can be calculated from eq. 3 as

F = (( 2205 lbm ) (1/32.17405 (slugs/ lbm )) ) (9.11 ft/s2)

= 624 lbf

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

ds = a dt2/ 2

= (9.11 ft/s2) (10 s)2/ 2

= 455 ft

The average acceleration work can be calculated from eq. 4 as

W = (624 lbf ) (455 ft)

= 284075 ft lbf

• 1 ft lbf = 1.36 J

The average acceleration power can be calculated from eq. 5 as

P = (284075 ft lbf ) / (10 s)

= 28407 ft lbf /s

• 1 ft lbf /s = 1.36 W = 0.00182 hp

Note that acceleration of a car varies due to gear shifts and motor characteristics.

Related Topics

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Motion of bodies and the action of forces in producing or changing their motion - velocity and acceleration, forces and torque.

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