# If a rocket with a mass of 4000 tons vertically accelerates at a rate of  6/5 m/s^2, how much power will the rocket have to exert to maintain its acceleration at 11 seconds?

Jan 4, 2016

P = 1.9 × 10^14 W

#### Explanation:

First we will calculate the thrust force of the rocket, then we will find the velocity of the rocket at 11 seconds and lastly calculate the power at 11 s required to maintain its acceleration at that velocity.

Thrust force (using simplified version of Newton’s second law):
Mass: m = 4000 tons = 4000 × 1000 kg = 4.0 × 10^6 kg
F = ma = 4.0 × 10^6 × 65 = 2.6 × 10^8 N

Velocity of the rocket at 11 s:
Use equation of constant acceleration, assuming it starts at rest.
s = ?
$u = 0$
v = ?
$a = 65 m {s}^{- 2}$
$t = 11 s$

Use v = u + at = 0 + 65 × 11 = 715 m s^(-1)

Power exerted at 11 s:
P = Fv = 2.6 × 10^8 × 715 = 1.859 × 10^14 = 1.9 × 10^14 W (2 sf)