The power P that must be delivered by a cars engine varies directly as the distance d that the car moves and inversely as the time t required to move that dista

Question

To move the car 2,100ft in 70s, the engine must deliver 180 kilowatts (kW) of power. Find the distance (in feet) the car moves when 204kW of power is delivered for 90s. Enter the answer as an integer. Round to the nearest whole unit.

Answer 1

P ∝ d

 

P ∝ 1/t

 

Using this information, we can establish a formula:

 

P = Kd/t  , where K is some constant

 

We need to determine that constant using the initial conditions.

 

d = 2100 ft

t = 70 s

P = 180 KW

 

K = Pt/d

K = [(180 kW)(70s)] / 2100 ft

K = 6 kW s / ft

 

We can now find the distance of the car when P = 204 kW and t = 90s

 

P = Kd/t

d = Pt/K

d = [(204 kW)(90 s)] / (6 kWs /ft)

d = 3060 ft

 

 

Notice that I included the units in the calculations.  This is a good method to ensure that formulas are correct.

 

Answer 2

p=kd/t

use info to solve for k

180=k(2100)/70

6=k

 

p=6d/t

204 = 6d/90

3060 ft=d