### Auto Motion

#### Power Requirements for Constant Speed and Constant Acceleration

For constant speed v, the net force must be zero:  F = fair + frolling

Power required to maintain speed v is:   P = Fv

Alternatively: W = F x and P = W/t = F (x/t) = F v.

For v = 30 m/s (≈ 65 mph),
fair ≈ 500 N , frolling ≈ 300 N → F ≈ 800 N.

Then P = F v = 800 x 30 = 24,000 W ≈ 32 hp !!

To move at constant acceleration a:  F - fair - frolling = ma

Typical numbers: 0 - 30m/s (≈ 65 mph) in 10 sec
→ a = 3 m/s2, and m= 1500 kg

Then F = ma + fair + frolling = 4500 + 300 + ( < 500)
→ max. force ≈ 5300 N.

Max. power (at top speed):
Pmax = Fmax vmax = 5300 x 30 = 160 KW ≈ 210 hp !!

#### Power and Acceleration

A car goes from 0 to 30 mph in 1.5 seconds. How long does it take the car to from from 0 to 60 mph? Assume that the power of the engine is velocity independent. Neglect friction and wind resistance.

1. 3 sec
2. 4.5 sec
3. 6 sec
4. 9 sec
5. 12 sec

Definition of power: P= dE/dt = d (½ mv2)/dt = constant.

This implies v2 ∝ t, or v ∝ t1/2.

Acceleration is decreasing in time!