How much retardation must be applied to stop a bus running at a uniform speed of 40km/h in 5 seconds?
-20/9
8m
To calculate the retardation required to stop a bus, we need to know the initial velocity (vâ‚€), the final velocity (v), and the time (t) it takes to stop. In this case, the initial velocity is 40 km/h, the final velocity is 0 km/h (since the bus is coming to a stop), and the time is 5 seconds.
First, let's convert the initial velocity from km/h to m/s, as it is the standard unit for calculating retardation. We know that 1 km/h is equal to 1/3.6 m/s.
So, vâ‚€ = 40 km/h = (40/3.6) m/s = 11.11 m/s
v = 0 m/s
t = 5 seconds
Now, we can use the formula for calculating retardation:
Retardation (a) = (v - vâ‚€) / t
Substituting the given values:
a = (0 - 11.11) / 5
a = -11.11 / 5
a = -2.22 m/s²
Therefore, the retardation required to stop the bus running at a uniform speed of 40 km/h in 5 seconds is -2.22 m/s². The negative sign indicates that the retardation is in the opposite direction of the initial velocity, which is necessary to bring the bus to a stop.
Convert km/h to m/s:
40 km/h * 1000 m/km * (1/3600) h/s = ____ m/s
Acceleration = Δ velocity / Δ time
= (0 m/s - ____ m/s) / 5 s
= ____ m/s ²