A Train with mass 40000 kg moving with a velocity of 60 m/s comes at rest in 10 sec by applying the brakes. What is the retardation of a train and force on the brake?
Answers
A train of mass 40000 kg moving with a velocity of 60 m/s comes at rest in 10 sec by applying the brakes.
We have to find the retardation of a train and force on the brake.
From above data we have; mass (m) is 40000 kg, initial velocity (u) is 60 m/s, final velocity is 0 m/s (as brakes are applied) and time (t) is 10 sec.
Using the First Equation Of Motion,
v = u + at
Substitute the known values in the above formula,
→ 0 = 60 + a(10)
→ -60 = 10a
Divide by 10 on both sides,
→ -60/10 = 10a/10
→ -6 = a
(Negative sign shows retardation)
Therefore, the acceleration of the train is 6 m/s².
Now, force is defined as the product of mass and acceleration i.e. F = ma.
Substitute the values,
→ F = 40000(-6)
→ F = -240000
Therefore, the force of -240000 N is applied.
GIVEN :
• M = 40000kg.
• V = 60m/s .
• T = 10sec.
TO FIND :
• What retardation of a train ?
• What Force apply on the brake ?
SOLUTION :
Case (I)
=> Applying, the First Equation Of Motion,
=> v = u + at
[ Put the values ]
=> 0 = 60+ a × 10
=> - 60 = a × 10
=> a = - 60 / 10
=> a = - 6m/s² .
.°. The retardation of a train is - 6 m/s² .
Case (II)
=> Using, Force formula,
=> F = ma
[ Put the values ]
=> F = 40000 × (-6)
=> F = -240000N .