Answer:
P = W / t = m g s / t = m g v    where work by auto = m g s
30 kw = 30000 watts = 30000 J / s
Work wasted = F v    as shown above relating work and power
Work done against incline = m g s sin 8.75 Â and power against incline
= m g v sin 8.75 = 1222 v Joules / sec
power in moving auto = power available - power lost to friction
power in moving auto = 30000 - resistance = 30000 - 910 v
1222 v = 30000 - 910 v
v = 30000 / 2132 = 14 m/s
Note: constant resistance to motion must mean P = W / t = F s / t = F v
Maximum speed will be v = 14.07 m/s
Power is defined time rate of doing work or delivering energy.
Work done = Force * displacement
Power = work done / time
      = (Force * displacement ) / time
since , displacement / time = velocity
Power  = force * (displacement / time ) = force  * velocity
Power = mass * acceleration * velocity ( Â as force = mass * acceleration)
since , car is travelling up in an incline of 8.75° to the horizontal
hence , it will have two components of velocity
vertical component = v sin (theta ) = v sin(8.75°)
horizontal component = v cos (theta)= v cos (8.75°)
Power = m* a * v sin (theta )
     = 820 * 9.8  * v *sin (8.75°)             ( a = g = 9.8 m[tex]/s^{2}[/tex])
     = 1221.472 v
Power lost due to resistance in motion  = 910 * velocity = 910 v
Power = Total power - power lost due to resistance in motion
      = 30 * [tex]10^{3}[/tex]  - 910 v
  Â
30 * [tex]10^{3}[/tex] Â - 910 v = 1221.472 v Â
v = 14.07 m/s
Maximum speed will be v = 14.07 m/s
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