Car A is traveling at 18 m/s and car B at 25 m/s. Car A is 300m behind car B when the driver of Car A accelerates his car with an acceleration of 1.80m/s^2.
How long does it take car A to overtake car B?
To find out how long it takes for car A to overtake car B, we need to calculate the time it takes for car A to cover the distance between them.
Let's break down the problem:
1. Determine the initial positions of both cars:
- Car A is 300 meters behind car B. Therefore, car A starts with a position of -300 meters, and car B starts at 0 meters.
2. Find the relative velocity between the two cars:
- Car A's velocity relative to car B is the difference between their velocities: (25 m/s - 18 m/s) = 7 m/s.
3. Determine the time it takes for car A to catch up to car B:
- We'll use the equation: distance = velocity × time + 0.5 × acceleration × time^2.
- In this case, the initial distance is -300 meters (because car A is behind car B), the initial velocity is 7 m/s (relative velocity), and the acceleration is 1.8 m/s^2 (acceleration of car A).
- Plugging these values into the equation, we get: -300 = 7t + 0.5 × 1.8 × t^2.
- Rearranging the equation, we get: 0.9t^2 + 7t + 300 = 0.
- We can now solve this quadratic equation to find the time it takes for car A to overtake car B.
Now we can solve the quadratic equation to find the time it takes for car A to overtake car B.