Answer:
The winner of the race is the boat because the it get to the goal a time of t=42.42 seg
Explanation:
The problem has tow steps the first one is the time takes each vehicule to get the top speed.
1.
[tex]V_{f} = V_{o} + a*t \\V_{o}= 0 \frac{m}{s} \\t = \frac{V_{f} }{a} \\t_{1} = \frac{41 \frac{m}{s} }{1.95 \frac{m}{s^{2} } }=21.02 s \\t_{2} = \frac{32 \frac{m}{s} }{6.5 \frac{m}{s^{2} } } =4.92 s[/tex]
2.
Now after they take the top speed have to know who get first to the goal
[tex]x_{f}= x_{o} + v_{o}*t + \frac{1}{2}* a *t^{2}\\ a=0 \frac{m}{s^{2} }\\ x_{o}= 0[/tex]
So the speed Vo is now the final velocity calculated before
[tex]t= \frac{x_{f} }{V_{o} } \\t1= \frac{1200m }{41\frac{m}{s} } = 29.2 s\\t2= \frac{1200m }{32\frac{m}{s} } = 37.5 s\\[/tex]
[tex]t1_{total}= 21.2+29.2=50.22 s\\ t2_{total}= 4.91+37.5=42.41 s[/tex]
