Two motorcars, A and B are appraching each other . At time t=0 car A and B are at 975m. With their speeds being 30m/s2 and 17m/s2 respectively and car A passed point b for 40s and car B passes at 42s after how long will the cars pass each other
To find out when the cars will pass each other, we need to compare the distances traveled by the two cars.
Let's start with car A. The equation for distance traveled by car A is given by:
dA = vAt + (1/2)at^2
where dA is the distance traveled by car A, vA is the initial velocity of car A, a is the acceleration of car A, and t is the time.
Similarly, for car B:
dB = vBt + (1/2)bt^2
where dB is the distance traveled by car B, vB is the initial velocity of car B, b is the acceleration of car B, and t is the time.
At the point of passing each other, the distance traveled by car A should be equal to the distance traveled by car B:
dA = dB
Substituting the equations for dA and dB, we get:
vAt + (1/2)at^2 = vBt + (1/2)bt^2
Rearranging and simplifying the equation, we have:
(vA - vB)t = (1/2)(b - a)t^2
Dividing both sides of the equation by (vA - vB), we find:
t = (1/2)(b - a)t^2 / (vA - vB)
Now let's plug in the given values:
vA = 30 m/s^2, a = 0 m/s^2 (since the car is already at its initial speed), vB = 17 m/s^2, and b = 17 m/s^2 (since car B is also at its initial speed).
t = (1/2)(17 - 0)t^2 / (30 - 17)
t = (1/2)(17)t^2 / (13)
t = 8.5t^2 / 13
To solve for t, let's bring all the terms to one side and solve the quadratic equation:
8.5t^2 / 13 - t = 0
(8.5t^2 - 13t) / 13 = 0
Now we can solve for t by factoring or using the quadratic formula. In this case, let's use factoring.
t(8.5t - 13) / 13 = 0
Setting each factor equal to zero, we have:
t = 0 or 8.5t - 13 = 0
Solving the second equation for t, we find:
8.5t = 13
t = 13 / 8.5
t ≈ 1.53 seconds
Therefore, the cars will pass each other approximately 1.53 seconds after the second car passes point B.
Note: It's important to check our answer to ensure it makes sense. In this case, we can confirm that car A passes point B at 40 seconds, and car B passes point B at 42 seconds. Since the cars are approaching each other, it makes sense that they would pass each other sometime between these two times.