Car Acceleration
Car acceleration calculator.
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.
mph
Car Acceleration Diagram  km/h
Download and Print Car Acceleration Chart
Car Acceleration Diagram  mph
Download and Print Car Acceleration Chart
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 average acceleration can be calculated from eq. 1 as
a = ((27.8 m/s)  (0 m/s)) / (10 s)
= 2.78 m/s^{2}
The average 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 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/s^{2}
In the Imperial system mass is measured in slugs where 1 slug = 32.17405 lb_{m}
The average 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 average 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 average 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
Note that acceleration of a car varies due to gear shifts and motor characteristics.
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