a red car and a green car, identical except for the color, move toward each other in adjacent lanes and parallel to an x axis. At time , the red car is at and the green car is at . If the red car has a constant velocity of 20 km/h, the cars pass each other at , and if it has a constant velocity of 40 km/h, they pass each other at . What are (a) the initial velocity and (b) the acceleration of the green car?
What numbers are supposed to follow the words "at" ?
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To solve this problem, we need to use the formula for calculating velocity and time. The formula for velocity is:
velocity = change in position / time
(a) To find the initial velocity of the green car, we need to find the change in position and divide it by the time.
Given that the red car has a constant velocity of 20 km/h, and at time t=3, the red car is at x=0 km, and the green car is at x=-35 km. The change in position for the green car is then:
change in position = final position - initial position
= (-35 km) - (0 km)
= -35 km
Next, we need to find the time it took for the green car to reach -35 km. From the problem, we know they pass each other at t=7. Therefore, the time it took for the green car to reach -35 km is:
time = t green - t red
= 7 - 3
= 4
Now we can calculate the initial velocity of the green car:
initial velocity = change in position / time
= -35 km / 4
= -8.75 km/h
Since the initial velocity is the rate at which the position changes with respect to time, a negative value indicates that the green car is moving in the opposite direction of the red car.
Therefore, the initial velocity of the green car is -8.75 km/h.
(b) To find the acceleration of the green car, we need to use the formula for calculating acceleration:
acceleration = change in velocity / time
Given that the red car has a constant velocity of 40 km/h, and at time t=5, the red car is at x=0 km, and the green car is at x=30 km. The change in velocity for the green car is then:
change in velocity = final velocity - initial velocity
= 40 km/h - (-8.75 km/h)
= 48.75 km/h
Next, we need to find the time it took for the green car to change its velocity. From the problem, we know they pass each other at t=5. Therefore, the time is:
time = t green - t red
= 5 - 5
= 0
Now we can calculate the acceleration of the green car:
acceleration = change in velocity / time
= 48.75 km/h / 0
= undefined
Since the time is 0, the acceleration is undefined. This implies that the green car does not have constant acceleration and is likely affected by outside forces or variables.
Therefore, the acceleration of the green car is undefined.