Question

A car has a mass of 2500 kg, and accelerates at 4.5 m/s2 starting from rest. If the drag resistance on the car due to the wind is FD = (3v1.5) N, where v is the velocity in m/s, determine (a) the average power supplied to the engine from rest at t = 0 and t = 5s, and (b) the power supplied to engine at t = 7

Answer 1

a) P = 454.05 kW

b) P = 637.938 kW

Step-by-step explanation:

The mass of the car, M = 2500 kg

Acceleration of the car, a = 4.5 m/s²

Drag resistance of the car,
`F_(D) = (3*1.5v) =4.5v N`

`\sum F = ma\\F - F_(D) = 2500*6\\F - 4.5v = 15000\\F = 15000 + 4.5v`

To calculate the value of the velocity, use the equation of motion:

v = u + at

At time t = 0, the car is at rest, u = o m/s

v = 0 + 6(5)

v = 30 m/s

F = 15000 + 4.5*30

F = 15,135 N

Power, P = Fv

P = (15135*30)

P = 454,050 W

P = 454.05 kW

b) power supplied to engine at t = 7 s

v = u + at

v = 0 + 7*6

v = 42 m/s

F = 15000 + 4.5v

F = 15000 + 4.5*42

F = 15,189 N

Power, P = Fv

P = 15189 * 42

P = 637938 W

P = 637.938 kW