A red car and a green car, identical except for color, move toward each other in adjacent lanes and parallel to an x-axis. At time t=0, the red car is at x sub r = 0 and the green car is at x sub g = 220m. If the red car has a constant velocity of 20km/h, the cars pass each other at x = 44.5m, and if it has a constant velocity of 40 km/h, they pass each other at x=76.6m. What are (a) the initial velocity and (b) the constant acceleration of the green car?
Use the two distances to calculate how long it takes then to pass each other.
For Vr = 20 km/h = 5.555 m/s, they pass after 44.5/5.555 = 8.01 seconds. At that time, the green car has traveled 220 - 44.5 = 175.5 m
For Vr = 40 km/h = 11.111 m/s, they pass after 76.6/11.111 = 6.894 s. at that time, the green car has traveled 220 - 76.6 = 143.4 m
Finally using those times and the corresponding distances traveled by the green car, solve two equations in two unknowns for Vo and a of the green car.
That step I leave up to you.
Thanks a bunch!
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To find the initial velocity and constant acceleration of the green car, we can use the equations of motion.
Let's start by finding the time it takes for the cars to meet.
For the first scenario where the red car has a velocity of 20 km/h, the relative velocity between the cars is the sum of their velocities, which gives us:
Relative velocity = Red car velocity - Green car velocity
Relative velocity = 20 km/h - Green car velocity
Since the cars pass each other at x = 44.5 m, we can use the equation of motion:
x = (initial velocity * time) + (0.5 * acceleration * time^2)
Substituting the values, we get:
44.5 = (0.5 * relative velocity * time)
Since we have the relative velocity and the time, we can solve for the time taken.
Now, let's solve for the time using the given values.
For the first scenario:
Relative velocity = 20 km/h - Green car velocity
Green car velocity = 20 km/h - Relative velocity
Substituting the values, we get:
44.5 = (0.5 * (20 km/h - Green car velocity) * time1)
Simplifying the equation, we get:
time1 = 89 m / (20 km/h - Green car velocity)
For the second scenario, we follow the same steps:
76.6 = (0.5 * (40 km/h - Green car velocity) * time2)
time2 = 153.2 m / (40 km/h - Green car velocity)
Now, we can equate the two expressions for time and solve for the initial velocity of the green car.
time1 = time2
89 m / (20 km/h - Green car velocity) = 153.2 m / (40 km/h - Green car velocity)
After solving this equation, we can determine the initial velocity of the green car.
(a) The initial velocity of the green car can be found by solving the equation above.
Moving on to finding the constant acceleration:
We know that the green car starts at x = 220 m and passes the red car at x = 44.5 m (using the first scenario). We can again use the equation of motion:
x = (initial velocity * time) + (0.5 * acceleration * time^2)
Substituting the values, we get:
44.5 = (initial velocity * time) + (0.5 * acceleration * time^2)
Now that we know the initial velocity from part (a), we can solve for acceleration using the equation above.
(b) The constant acceleration of the green car can be found by solving the equation above.
Please note that the unit conversions (e.g., km/h to m/s) may be required to ensure consistent units for the calculations.