Question

The driver of a train which is moving at a speed of 60kmph sights another stationary train on the same track 100m ahead and immediately applies brakes determine the retardation if the accident is to be just avoided and the time it takes to stop

Answer 1

Answer:

• Speed of train ¹ = 60 km/h
• Distance = 100 m
• Acceleration to be applied so that an accident is avoided?

$\displaystyle\underline{\bigstar\:\textsf{According to the given Question :}}$

• Here we shall find the initial velocity Which will be the velocity of train¹ - train²

$\displaystyle\sf :\implies u = v_1-v_2$

$\displaystyle\sf :\implies u = 60-0$

$\displaystyle\sf :\implies u = 60 \ km/h$

• Then we shall use the third Equation if motion to find the acceleration of the body as we have the initial, the final and the distance to be travelled

$\displaystyle\sf \dashrightarrow v^2-u^2 = 2as$

• v = Initial Velocity = 0 m/s
• u = Final Velocity = 60 × 5/18 = 16.7 m/s
• s = Distance = 100 m
• a = Acceleration = ?

$\\\displaystyle\sf \dashrightarrow 0^2-16.7^2 = 2\times a\times 100$

$\displaystyle\sf \dashrightarrow 0-278.89 = 200a$

$\displaystyle\sf \dashrightarrow -278.89 = 200a$

$\displaystyle\sf \dashrightarrow \dfrac{-278.89}{200} = a$

$\displaystyle\sf \dashrightarrow\underline{\boxed{\sf Acc^n = -1.3 \ m/s^2}}$

$\displaystyle\therefore\:\underline{\textsf{The retardation will be \textbf{ 1.3 m}}\sf{/} \textsf{\textbf{s}} \sf {}^2}$