The problem is as follows:
A VW bus is ascending over a ramp as indicated in the figure from below. The bus has a power of $120\,kW$ to ascend over the incline. If the friction with the road and air is $\frac{3}{25}$ of its weight. Find the speed which the bus is ascending in kilometers per hour. Assume that the mass of the bus is $2t$.
The alternatives in my book are as follows:
$\begin{array}{ll} 1.&108\,\frac{km}{h}\\ 2.&90\,\frac{km}{h}\\ 3.&72\,\frac{km}{h}\\ 4.&36\,\frac{km}{h}\\ 5.&54\,\frac{km}{h}\\ \end{array}$
I'm totally lost in this question because of the fact that the mass seems to be changing with time as it is given $2t$
In the case to find the speed the only formula which comes to my mind is:
$P=F\cdot v$
But what force should it be assumed here?. Can someone help me?.
If the speed is held constant then this means that the force is:
$F= f_{frictional}$
$F=\frac{3}{25}mg$
But I dont' know what else can be used as I think there will be an integration. Can someone give me some help with this?.
The mass of the bus is 2 metric tonnes = 2000 kg. It is constant.
The engine is supplying power to move the bus up the incline against friction : $$P_1=\frac{3}{25}mgv$$ It is also supplying power to raise the bus vertically against gravity : $$P_2=mgv\sin\theta$$ The total power supplied by the engine is $P_1+P_2$. No integration required. Probably more suitable for Physics SE.