The train slows down uniformly from a speed of 50m/s to a speed of 10m/s in a time of 20sec,During the next 30sec,it accelerates uniformly to a speed of u metres/sec.calculate the retardation from t=0 to t=20?
Lol, this website censors the "r-word" which is needed for this question, so it reduced it down to only show "ation".
since it slowed by 40m/s in 20s, that's
-40m/s / 20s = -2m/s^2
Easy Way (using the definition of acceleration/retardation):
a = Δv / Δt
Δv = vf - vi = 10 m/s - 50 m/s = -40 m/s
Δt = tf - ti = 20 s - 0 s = 20 s
a = Δv / Δt
a = (-40 m/s) / (20 s)
a = -2 m/s²
Harder Way (from a motion equation):
vi = 50 m/s,
vf = 10 m/s,
Δt = 20 s,
a = ?
vf = vi + a(Δt)
vf - vi = a(Δt)
a = (vf - vi) / Δt
a = (10 - 50) / 20
a = (-40) / 20
a = -2 m/s²
To calculate the retardation from t = 0 to t = 20, we need to determine the change in velocity and the time interval.
Given:
Initial speed, u₁ = 50 m/s
Final speed, u₂ = 10 m/s
Time interval, t = 20 seconds
Retardation is defined as the negative acceleration, which can be calculated using the formula:
Acceleration = (Final speed - Initial speed) / Time interval
Using the given values, we can calculate the retardation:
Acceleration = (u₂ - u₁) / t
= (10 - 50) / 20
= (-40) / 20
= -2 m/s²
Therefore, the retardation from t = 0 to t = 20 is -2 m/s².