please provide the calculation steps What speed will a truck with a mass/power r

Question

please provide the calculation steps

What speed will a truck with a mass/power ratio of 275 kg/kW pulling off from a standing start attain after travelling a distance of 400 m along a grade of +2%. What will its maximum speed be on this same grade? 5. (a) Answer:[38 km/h 43,5 km/h] (b) How far will the same truck starting at a speed of 80 km/h at the bottom of a +4% grade travel before it slows down to 47 km/h? Answer: [700 m] What will its terminal speed be if this grade is continued over a distance greater than say 2000 m? (c) Answer: [27,6 km/h]

Explanation / Answer

I would start by calculating how much force you would need, to accelerate this 300 kg vehicle to the speed you want, in the time you want, using the familiar F = ma.

Now you know how much force has to be applied, and you know that this force will be applied via wheels of 20 cm radius.

So, torque at the wheels will be tau = F * r, where F is whatever you decided in the first step, and r is 20 cm.

(Tau = F*r*sin[theta], where theta can be assumed to be 90 degrees, where the wheel contacts the road surface.)

If the wheels incorporated their own integral electric motor, you would have the answer right there. You would know the torque and the time you need to apply it, to reach the speed in the necessary amount of time. After which, ideally, on a flat surface, no wind drag and no friction, no more torque is needed, you just coast along.

If the motor is separate, geared to the wheels, then you can reduce the torque required of the motor by selecting the appropriate gear ratio. For example, a 2:1 gear ratio would require half as much torque from the motor as is being applied at the wheels.

As to speed, the circumference of the 20 cm (radius) wheel is as far as the vehicle moves in one wheel rotation. C = 2*pi*r

So now you know that C = distance traveled per rotation, and at one rpm, that distance would be traveled in one minute. So you have the relationship between rpm and speed. You can scale the wheel rpm up or down, to calculate the wheel rpm needed to move at the the speed you need to go.

Once you have the wheel rpm needed to reach your desired speed, it's a simple matter of multiplying that by the gear ratio, to calculate the motor rpm needed to travel at that speed.

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