Answer
It would take 7.5 seconds to accelerate from 55 km/h to 95 km/h.
Work Step by Step
Changing the velocities to meters per second:
$v_1 = (35~km/h)(\frac{1000~m}{1~km})(\frac{1~h}{3600~s}) = 9.7~m/s$
$v_2 = (65~km/h)(\frac{1000~m}{1~km})(\frac{1~h}{3600~s}) = 18.1~m/s$
Now, we find the power:
$P = \frac{\Delta E}{\Delta t} = \frac{\frac{1}{2}(m)(v_2^2-v_1^2)}{t}$
$P = \frac{\frac{1}{2}(1300~kg)((18.1~m/s)^2-(9.7~m/s)^2)}{3.8~s}$
$P = 39,940~W$
We can use this power to find the time to accelerate from 55 km/h to 95 km/h:
$v_1 = (55~km/h)(\frac{1000~m}{1~km})(\frac{1~h}{3600~s}) = 15.3~m/s$
$v_2 = (95~km/h)(\frac{1000~m}{1~km})(\frac{1~h}{3600~s}) = 26.4~m/s$
$P = \frac{\Delta E}{\Delta t} = \frac{\frac{1}{2}(m)(v_2^2-v_1^2)}{t}$
$t = \frac{\frac{1}{2}(1300~kg)((26.4~m/s)^2-(15.3~m/s)^2)}{39,940~W}$
$t = 7.5~s$
It would take 7.5 seconds to accelerate from 55 km/h to 95 km/h.