If an automobile engine delivers 45.2 hp of power, how much time will it take for the engine to do 5.40 105 J of work? (Hint: Note that one horsepower, 1 hp, is equal to 746 watts.) in seconds

P = 45.2hp * 746W/hp = 33,719. Watts =

33,719 Joules/s.

t=(5.4*10^5J/3.3719*10^4J) * 1s.=16.0s.

To solve this problem, we can use the formula:

work = power × time

We are given that the power is 45.2 hp and the work is 5.40 × 10^5 J. We need to find the time.

First, let's convert the power from horsepower to watts using the conversion factor given in the hint.

1 hp = 746 watts

So, 45.2 hp = 45.2 × 746 watts.

Substituting the values into the formula:

5.40 × 10^5 J = (45.2 × 746 watts) × time

Now, let's solve for time.

time = (5.40 × 10^5 J) / (45.2 × 746 watts)

time = (5.40 × 10^5 J) / (33839.2 watts)

time ≈ 15.95 seconds

Therefore, it will take approximately 15.95 seconds for the engine to do 5.40 × 10^5 J of work.

To find the time it will take for the engine to do 5.40 x 10^5 J of work, we can use the formula:

Work = Power x Time

Given:
Power of the engine = 45.2 hp
Work to be done = 5.40 x 10^5 J

First, let's convert the power from horsepower to watts using the conversion factor given in the hint.
1 hp = 746 watts

Power in watts = 45.2 hp x 746 watts/hp (using the conversion factor)

Power in watts = 33699.2 watts

Now, we can rearrange the formula to solve for time:

Time = Work / Power

Substituting the given values:
Time = (5.40 x 10^5 J) / (33699.2 watts)

Calculating this, we find:
Time = 16.04 seconds (rounded to two decimal places)

Therefore, it will take approximately 16.04 seconds for the engine to do 5.40 x 10^5 J of work.