Two cars approach each other from an initial distance of 2400 m. Car A is moving to the E at a constant rate speed of 40ms. Car B is moving to the W at a speed of 10ms but is accelarating at a rate of 2.00ms^2.
What is the time before the cars meet
the distance a traveled before meeting b
the relative speed at which the cars hit.
Call x = 0 the location were Car A starts. Call that car's location X1.
Car B then starts at x = 2400. Call its location X2
X1 = 40 t
X2 = 2400 - 10 t - t^2.
They meet when X1 = X2.
40t = 2400 -10 t - t^2
Rearrange that to read
t^2 +50 t -2400 = 0
(t +80)(t-30) = 0
Solve for the time t that is a positive root of that equation.
Use that value of t to solve for the location where they meet. The relative velocity is V1 - V2. But V2 is negative, so you end up adding the speeds of the cars at time t.
To find the time before the cars meet, we can use the concept of relative velocity.
First, let's consider the velocity of Car B. Since it is accelerating at a constant rate, we can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
We know that the initial velocity of Car B (u) is 10 m/s, the acceleration (a) is 2.00 m/s^2, and we need to find the time (t). The final velocity is unknown but is not required to find the time.
Using the equation v = u + at, we can rearrange it to solve for time:
t = (v - u) / a
As Car B is moving to the west, its velocity is negative. So we have:
t = (-10 m/s - 0 m/s) / (-2.00 m/s^2)
t = 5 seconds
Therefore, it will take 5 seconds before the cars meet.
To find the distance Car A travels before meeting Car B, we can use the formula s = vt, where s is the distance, v is the velocity, and t is the time.
Since Car A is moving to the east at a constant velocity of 40 m/s, and the time it takes for the cars to meet is 5 seconds, we can plug these values into the formula:
s = 40 m/s * 5 s
s = 200 meters
Therefore, Car A travels a distance of 200 meters before meeting Car B.
To find the relative speed at which the cars hit, we can simply add up their velocities.
Car A is moving to the east at a speed of 40 m/s, and Car B is moving to the west at a velocity of -10 m/s (since it is moving in the opposite direction). Adding these velocities together:
Relative speed = 40 m/s + (-10 m/s)
Relative speed = 30 m/s
Therefore, the relative speed at which the cars hit is 30 m/s.