A train travelling at 20m/s undergoes a uniform retardation of 2m/s when the break are applied calculate the time taken when it comes to rest and the distance travelled from the place where the breaks are applied
v = 20 - 2t
t = 10 s
s(t) = 20t - t^2
s(10) = 20*10 - 10^2 = 100 m
True
To calculate the time taken for the train to come to rest when the brakes are applied and the distance traveled from the place where the brakes are applied, we can use the equations of motion.
First, let's identify the given values:
Initial velocity (u) = 20 m/s
Acceleration (a) = -2 m/s² (negative sign indicates retardation)
Final velocity (v) = 0 m/s (since the train comes to rest)
Distance traveled (s) = ?
We'll use the equation:
v² = u² + 2as
Rearranging the equation, we have:
s = (v² - u²) / (2a)
Plugging in the known values:
s = (0² - 20²) / (2 * -2)
s = (-400) / (-4)
s = 100 meters
Therefore, the distance traveled from the place where the brakes are applied is 100 meters.
Now, let's find the time taken for the train to come to rest using the equation:
v = u + at
Rearranging the equation, we have:
t = (v - u) / a
Plugging in the known values:
t = (0 - 20) / -2
t = 20 / 2
t = 10 seconds
Therefore, the time taken for the train to come to rest when the brakes are applied is 10 seconds.