homework and exercises - How long does it take for an electric car to go from 0 to 60 mph?

I found the freefall motion equation which describes terminal velocity of a falling body, but I can't find a similar equation for a vehicle subject to constant traction force, so I tried determining it by myself, but resulting equation is not plausible, as it shows dozens of seconds needed for a 1600 kg vehicle to go from 0 to 60 mph, so there must be something wrong. I'm using this equation:

$$v(x) = v_f \cdot \tanh\left(\frac F {mv_f} \cdot x \right) = v_f \cdot\tanh\left(\frac {T/w } {m v_f} \cdot x \right)$$

• $v_f$ = terminal velocity = $\sqrt {\frac F c} = \sqrt {\frac {T} {wc}}$


• $c = \frac 1 2 \rho C_d A$


• $\rho$ = air density = 1.225 $\frac {kg} {m^3}$


• $C_d$ = air drag coefficient = 0.32


• A = frontal area = 2.19 m$^2$



• T = given torque = 220 Nm


• w = wheel radius = 0.25 m


• m = vehicle mass = 1762.5 kg

Freefall motion equation is:

$$v(x) = v_f \tanh\left( {x\sqrt{\frac{gc}{m}}}\right)$$

with $v_f=\sqrt{\frac{mg}c}$

With above data for the car, I should get around 10s time for 0-60 mph, but I get 63 seconds!

What am I doing wrong?

With above data(1) for the car, I know (2) I should get around 10s time for 0-60 mph, but I get 63 seconds!

What am I doing wrong?

Other literature data:

• Fiat Stilo - 255 Nm, 1488 kg, 11.2 s


• BMW M3 - 400 Nm, 1885 kg, 5.3 s


• Citroen C3 - 133 Nm, 1126 kg, 14.5 s

Literature data for electric cars:

• kg W Nm sec-to-60mph



• Chevrolet Volt 1715 63 130 9,0


• smart fortwo electric drive 900 55 130 12,9


• Mitsubishi i-MiEV 1185 47 180 13,5


• Citroen zEro 1185 49 180 13,5


• Peugeot iOn 1185 47 180 13,5


• Toyota Prius Plug-in 1500 60 207 10,7


• Renault Zoe 1392 65 220 8,0


• Renault Fluence Z.E. 1543 70 226 9,9


• Nissan leaf 1595 80 280 11,9


• Toyota RAV4 EV (US only) 1560 115 296 8,0

(1) "Evaluation of 20000 km driven with a battery electric vehicle" - I.J.M. Besselink, J.A.J. Hereijgers, P.F. van Oorschot, H. Nijmeijer

(2) http://inhabitat.com/2015-volkswagen-e-golf-electric-car-arrives-in-the-u-s-next-fall/2015-vw-e-golf_0003-2/