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erma4kov [3.2K]
3 years ago
13

Car A is traveling at 18.0 m/s and car B at 25.0 m/s. Car A is 300 m behind car B when the driver of car A accelerates his car w

ith an acceleration of 1.80 m/s2. How long does it take car A to overtake car B
Physics
1 answer:
goblinko [34]3 years ago
5 0

Answer:

car A reaches and immediately overtakes the car B at 22.56 s.

Explanation:

After car A accelerate at 1.8 m/s2, it travels a distance x(A) and car B will have travels a distance x(B), let's recall that the initial distance between them is 300 m, so we have:

x_{A}=300+x_{B}

Now, we can rewrite this equation in terms of speed and time

V_{iA}t+\frac{1}{2}at^{2}=300+V_{iB}t

Where:

V(iA) is the initial speed of car A

V(iB) is the initial speed of car B

t is the time when car A reaches the car B

a is the acceleration

18t+\frac{1}{2}1.8t^{2}=300+25t

0.9t^{2}-7t-300=0  

Solving this quadratic equation for t, and taking just the positive value, we will have:

t=22.56 s

Therefore, car A reaches and immediately overtakes the car B at 22.56 s.

I hope it helps you!

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