Find the power of a boat that accelerated

[jehan4141]

A 3.5x10⁷ kg ship is traveling at 7 m/s. The ship is accelerated forward with a F of 4.5 x 10⁵ N over a distance of 2 km.

What is the final speed? V_f = 10 m/s

How long does it take the ship to traverse the 2 km? T = 233.33 seconds

What is the average power which the engines had to produce to accelerate the ship in part 1? I need help on this please.

You can do P = W/t = (4.5x10⁵ x 2000) / 233.333

P = 3.9 x 10⁶ watts which is the right answer.

However, how come you can't do P = (F)(avg velocity)

P = 4.5x10⁵ * (3/2) = 675000 watts??

 

[cepheid]

Hi,

Where'd you get your avg velocity from?

You can use this formula, and in fact the two methods are equivalent, since:

P = W/t = Fd/t = F(d/t) = Fv_avg

v_avg = d/t = 2000 m / 233.33 s = 8.57 m/s

4.5e5 N * 8.57 m/s = 3.9e6 Nm/s (= J/s = W)

 

[cepheid]

Ah I see. It looks like you were confused in your formula for avg. velocity. It's (v_f + v_i)/2 NOT (v_f - v_i)/2.

(10 m/s + 7 m/s)/2 = 17/2 m/s = 8.5 m/s

 

[jehan4141]

Ah I see. It looks like you were confused in your formula for avg. velocity. It's (v_f + v_i)/2 NOT (v_f - v_i)/2.

(10 m/s + 7 m/s)/2 = 17/2 m/s = 8.5 m/s

Oh my goodness! Your eyes are so good! I have been using energy formulas all day that do Xf-Xi all day! Such a silly mistake thank you so much! it is so late and my brain if frazzled :)