Calculate top speed of vehicle [closed]

I'm trying to figure out the top speed of a vehicle and the time it would take to get there.

• Mass $$m = 200 \, \mathrm{kg} ;$$

• Engine power $$= 1000 \, \mathrm{W} ;$$

• Combined forces of friction and air and road resistances $$F_{\text{r}} = 40 \, \mathrm{N}$$ (ignoring slope).

For the purpose I am calculating the work that needs to be done for values $$v$$ from $$1$$ to $$100.$$ $$W = 0.5 m v^2$$

Then I'm calculating the time it would need, knowing the engine's power using $$P = \frac{W}{t} \qquad \Rightarrow \qquad t = \frac{W}{P}$$

Knowing the time I calculate the acceleration,$$a = \frac{v}{t} \,.$$

You can see results in the table below, ignore forces because they are just the product of more miscalculation

V, m/s  V, km/h t, s    a, m/s2 W, J        F1, N   F2, N
1.00    3.60    0.10    10.00   100.00      960.00  2000.00
2.00    7.20    0.40    5.00    400.00      460.00  1000.00
3.00    10.80   0.90    3.33    900.00      293.33  666.67
4.00    14.40   1.60    2.50    1600.00     210.00  500.00
5.00    18.00   2.50    2.00    2500.00     160.00  400.00
6.00    21.60   3.60    1.67    3600.00     126.67  333.33
7.00    25.20   4.90    1.43    4900.00     102.86  285.71
8.00    28.80   6.40    1.25    6400.00     85.00   250.00
9.00    32.40   8.10    1.11    8100.00     71.11   222.22
10.00   36.00   10.00   1.00    10000.00    60.00   200.00
11.00   39.60   12.10   0.91    12100.00    50.91   181.82
12.00   43.20   14.40   0.83    14400.00    43.33   166.67
13.00   46.80   16.90   0.77    16900.00    36.92   153.85
14.00   50.40   19.60   0.71    19600.00    31.43   142.86
15.00   54.00   22.50   0.67    22500.00    26.67   133.33
...
25      90      62.5    0.4     62500       0       80

Obviously I'm mistaken somewhere because acceleration never reaches 0 and speed just keeps going up and up.

closed as off-topic by David Z♦Oct 12 '18 at 1:29

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When at top speed, the power being expended by the car is given by:$$P= F \times v$$where F is the force being exerted and v is the velocity.
Given the constant retarding force that must be overcome, and the constant power output; we get:$$1000 = 40\times v$$or$$v=25 \text{ m/s}$$
So the maximum velocity of the car is $$25 m/s$$. That is, the engine could maintain a velocity of $$25$$ m/s.
Unfortunately, the force available from the constant power output engine decreases as the car's velocity increases from rest towards $$25$$ m/s, so the final velocity is approached asymptotically as the engine force decreases to $$40$$ N. IOW, the car never reaches this velocity, but gets as close as you want, if you're willing to wait...