Question

A car on a straight flat road races a boat on a calm canal parallel to the road. The car has a constant acceleration of 1.95m/s2 and reaches a top speed of 41.0m/s. The boat has a constant acceleration of 6.50m/s2 and reaches a top speed of 32.0m/s. The car and the boat accelerate to their top speed and then maintain their top speed for the rest of the rest. They race for 1.2km. which vehicle wins the race?

Answer 1

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.

$V_{f} = V_{o} + a*t \\V_{o}= 0 \frac{m}{s} \\t = \frac{V_{f} }{a} \\t_{1} = \frac{41 \frac{m}{s} }{1.95 \frac{m}{s^{2} } }=21.02 s \\t_{2} = \frac{32 \frac{m}{s} }{6.5 \frac{m}{s^{2} } } =4.92 s$

2.

Now after they take the top speed have to know who get first to the goal

$x_{f}= x_{o} + v_{o}*t + \frac{1}{2}* a *t^{2}\\ a=0 \frac{m}{s^{2} }\\ x_{o}= 0$

So the speed Vo is now the final velocity calculated before

$t= \frac{x_{f} }{V_{o} } \\t1= \frac{1200m }{41\frac{m}{s} } = 29.2 s\\t2= \frac{1200m }{32\frac{m}{s} } = 37.5 s$

$t1_{total}= 21.2+29.2=50.22 s\\ t2_{total}= 4.91+37.5=42.41 s$