A Train is travelling at 80km/h when it approaches a slower train 50m ahead in the same direction at 25km/h. If the faster train begins decelerating At -2.1m² while the slower train continues at constant speed, how soon and at what relative speed will they collide?
(Plz explain briefly)
Non-helpful answers will be reported
Tyssmm
Share
Answer:
To solve this problem, we need to use the equations of motion for the two trains and find the time and relative speed when they collide.
Let's first convert the speeds of the two trains from km/h to m/s:
The faster train is traveling at 80 km/h = 22.22 m/s
The slower train is traveling at 25 km/h = 6.94 m/s
Let's also define the initial position of the faster train as x1 = 0 m and the initial position of the slower train as x2 = 50 m.
Now, let's find the time when the two trains collide. We can use the following equation of motion for the faster train, where v1 is the velocity of the faster train, a1 is the acceleration of the faster train, and t is time:
x1 = v1*t + (1/2)a1t^2
We know that the initial velocity of the faster train is v1 = 22.22 m/s, and the acceleration is a1 = -2.1 m/s^2. We want to find the time when the faster train reaches the slower train, which is when their positions are the same, so we can set x1 = x2 and solve for t:
22.22t - 1.05t^2 = 50
This is a quadratic equation, which we can solve using the quadratic formula:
t = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = -1.05, b = 22.22, and c = -50. Solving for t, we get two solutions:
t = 4.122 s or t = 15.298 s
We can discard the second solution, since it implies that the faster train has passed the slower train and is moving away from it. Therefore, the two trains will collide in approximately 4.122 seconds.
Now, let's find the relative speed of the two trains at the moment of collision. The velocity of the faster train at that moment is given by:
v1 = 22.22 - 2.1*t
Substituting t = 4.122 s, we get:
v1 = 13.69 m/s
The velocity of the slower train is constant at 6.94 m/s. Therefore, the relative speed of the faster train with respect to the slower train at the moment of collision is:
v_rel = v1 - v2
v_rel = 13.69 - 6.94
v_rel = 6.75 m/s
So, the two trains will collide with a relative speed of 6.75 m/s.
Explanation: