A car accelerates from rest to a speed of 10 m/s in 20 seconds, what is the acceleration of the 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 

   = (vf - vs) / 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)

vs = 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

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Car Acceleration Diagram - mph

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

a = 2 ds / dt2                                 (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, 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 acceleration can be calculated from eq. 1 as

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

   = 2.78 m/s2

The 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 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/s2

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

The 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 acceleration work can be calculated from eq. 4 as

W = (624 lbf) (455 ft)

    = 284075 ft lbf

The 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

a car accelerates from rest to a speed of 10 m/s in 20 seconds. what is the acceleration of the car?

Answer:

Solution:

Formula: A = Δv/Δt

• A = Δv/Δt
• A = 10 m/s (20sec)
• A = 200 m/s²

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