Answer:
a) The final velocity is 28.0 m/s
b) It will take 50.9 s to come to a stop from a velocity of 28.0 m/s
c) In the first case ( point "a") the train will travel 7.68 × 10³ m. In the secid case, the train will travel 713 m
Explanation:
The equations for the position and velocity of objects moving in a straight line are as follows:
x = x0 + v0 • t + 1/2 • a •t²
v = v0 + a • t
Where
x = position at time t
x0 = initial position
v0 = initial velocity
t = time
a = acceleration
v = velocity at time t
a) Using the equation of velocity:
v = v0 + a • t
v = 4.00 m/s + 0.0500 m/s² • 480 s
v = 28.0 m/s
b) Now, the initial velocity is 28.0 m/s and the final velocity is 0 m/s. Then:
0 m/s = 28.0 m/s - 0.550 m/s²• t
-28.0 m/s / - 0.550 m/s² = t
t = 50.9 s
c) Now, we have to use the equation for the position of the train.
x = x0 + v0 • t + 1/2 • a •t² (let´s place the center of the frame of reference at x0. In this way, x0 = 0)
In the first case:
x = 4.00 m/s • 480 s + 1/2 • 0.0500 m/s² • (480 s)²
x = 7.68 × 10³ m
In the second case:
x = 28.0 m/s • 50.9 s - 1/2 • 0.550 m/s² • (50.9 s)²
x = 713 m
