348.34 m/s. When Superman reaches the train, his final velocity will be 348.34 m/s.
To solve this problem, we are going to use the kinematics equations for constant aceleration. The key for this problem are the equations [tex]d=v_{0} t+\frac{at^{2} }{2}[/tex] and [tex]v_{f} =v_{0} +at[/tex] where [tex]d[/tex] is distance, [tex]v_{0}[/tex] is the initial velocity, [tex]v_{f}[/tex] is the final velocity, [tex]t[/tex] is time, and [tex]a[/tex] is aceleration.
Superman's initial velocity is [tex]v_{0}=54.5\frac{m}{s}[/tex], and he will have to cover a distance d = 850m in a time t = 4.22s. Since we know [tex]d[/tex], [tex]v_{0}[/tex] and [tex]t[/tex], we have to find the aceleration [tex]a[/tex] in order to find [tex]v_{f}[/tex].
From the equation [tex]d=v_{0} t+\frac{at^{2} }{2}[/tex] we have to clear [tex]a[/tex], getting the equation as follows: [tex]a=\frac{2(d-v_{0}t) }{t^{2} }[/tex].
Substituting the values:
[tex]a=\frac{2(850m-54.5\frac{m}{s}.4.22s) }{(4.22s)^{2}}=69.63\frac{m}{s^{2}}[/tex]
To find [tex]v_{f}[/tex] we use the equation [tex]v_{f} =v_{0} +at[/tex].
Substituting the values:
[tex]v_{f} =54.5\frac{m}{s} +(69.63\frac{m}{s^{2}}.4.22s)=348.34\frac{m}{s}[/tex]
Superman is flying 54.5 m/s when he sees a train about to fall into a river 850 m away. He reaches the train in 4.22 s.then his final velocity would be 201.42 m/s
The total distance covered by any object per unit of time is known as speed. It depends only on the magnitude of the moving object. The unit of speed is meter/second. The generally considered unit for speed is a meter per second.
The mathematical expression for speed is given by
speed = total distance /Total time
As given in the problem Superman is flying 54.5 m/s when he sees a train about to fall into a river 850 m away. He reaches the train in 4.22 s.
Total distance covered by superman = 850 m
total time = 4.22 s
speed = 850/4.22 m/s
= 201.42 m/s
Thus, Superman is flying 54.5 m/s when he sees a train about to fall into a river 850 m away. He reaches the train in 4.22 s.then his final velocity would be 201.42 m/s
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