If a rocket with a mass of $7 k g$ $7 kg$ vertically accelerates at a rate of $\frac{3}{2} \frac{m}{s^{2}}$ $3/2 m/s^2$ , how much power will the rocket have to exert to maintain its acceleration at 6 seconds?

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Answer 1 · 2017-07-19T05:24:00

The power is $= 94.5 W$ $=94.5W$

We apply Newton's Second Law to find the force

$F = m a$ $F=ma$

The mass is $m = 7 k g$ $m=7kg$

The acceleration is $a = \frac{3}{2} m s^{- 2}$ $a=3/2ms^-2$

The force is

$F = m a = 7 \cdot \frac{3}{2} = \frac{21}{2} N$ $F=ma=7*3/2=21/2N$

We apply the equation of motion

$v = u + a t$ $v=u+at$

to calculate the speed at $t = 6 s$ $t=6s$

$v = 0 + \frac{3}{2} \cdot 6 = 9 m s^{- 1}$ $v=0+3/2*6=9ms^-1$

The power is

$P = F v$ $P=Fv$

$P = \frac{21}{2} \cdot 9 = 94.5 W$ $P=21/2*9=94.5W$

If a rocket with a mass of 7kg7 kg vertically accelerates at a rate of 32ms2 3/2 m/s^2, how much power will the rocket have to exert to maintain its acceleration at 6 seconds?