A train travelling at 30km/h stops when it's brakes are applied. The train suffers a deceleration our 2m/s.
@. How long does the train take to come to rest?
b) what is its final velocity?
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To find the time it takes for the train to come to rest, 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 taken.
In this case, the initial velocity (u) is 30 km/h, which we need to convert to m/s. To convert km/h to m/s, simply divide by 3.6:
u = 30 km/h / 3.6 = 8.33 m/s
The acceleration (a) is -2 m/s² (negative because it is deceleration).
The final velocity (v) is 0 m/s since the train comes to rest.
Substituting these values into the equation, we have:
0 = 8.33 m/s + (-2 m/s²) * t
Simplifying the equation:
-8.33 m/s = -2 m/s² * t
Dividing both sides of the equation by -2 m/s²:
t = -8.33 m/s / -2 m/s²
t = 4.165 s
Therefore, the train takes approximately 4.165 seconds to come to rest.
To find the final velocity (v), we can use the formula:
v = u + at
Using the same values for u, a, and t as before:
v = 8.33 m/s + (-2 m/s²) * 4.165 s
v = 8.33 m/s - 8.33 m/s
v = 0 m/s
Therefore, the final velocity of the train is 0 m/s.