A train is moving with a velocity of 20 m/s . when the brakes are applied , the acceleration is reduce to -0.5m/s2 . calculate the distance covered by the train before coming to rest.
every second v decreases by 1/2 m/s
so, it takes 40 seconds to stop
The distance covered during time t is
s = 20t - 1/4 t^2
Now just plug in t=40
To find the distance covered by the train before coming to rest, you can use the equation of motion:
v^2 = u^2 + 2as
where:
v = final velocity (0 m/s, since the train comes to rest)
u = initial velocity (20 m/s)
a = acceleration (-0.5 m/s^2)
s = distance covered
Rearranging the equation, we can solve for s:
s = (v^2 - u^2) / (2a)
Plugging in the values:
s = (0^2 - 20^2) / (2 * -0.5)
First, simplify the numerator:
s = (-400) / (2 * -0.5)
Then simplify the denominator:
s = (-400) / (-1)
Finally, solve for s:
s = 400 meters
Therefore, the train will cover a distance of 400 meters before coming to rest.