Question

A train is travelling at a speed of 90kmph. Brakes are applied so as to produce a uniform acceleration of \[-0.5m{{s}^{-2}}\] . Find how far the train will go before it comes to rest.
(A). \[625m\]
(B). \[4050m\]
(C). \[8100m\]
(D). \[1250m\]

Answer 1

Hint: As acceleration is constant, using equations of motion, we can calculate the distance covered by substituting the corresponding values. Convert the units as required. Negative acceleration means that the train is coming to a rest, this means that the final velocity will be zero.

Formula used:
 \[{{v}^{2}}={{u}^{2}}+2as\]

Complete step by step solution:
The initial speed of the train is \[90\,km\,h{{r}^{-1}}\] converting it into SI system, we get,
 \[\dfrac{90\times 1000m}{1\times 3600s}=25m{{s}^{-1}}\]
As the train is moving with constant deceleration, the distance covered by it can be calculated using the formula-
 \[{{v}^{2}}={{u}^{2}}+2as\]
Here,
 \[v\] is the final velocity
 \[u\] is the initial velocity
 \[a\] is acceleration
 \[s\] is the distance covered
As the train is coming to a rest,
 \[v=0\,m{{s}^{-1}}\]
Substituting values in the above equation, we get,
 \[\begin{align}
  & 0={{(25)}^{2}}-2\times 0.5\times s \\
 & s=625m \\
\end{align}\]
 The total distance covered by the train before coming to rest is \[625\,m\] .

So, the correct answer is “Option A”.

Additional Information: The SI system or the international system of units is the most commonly used system of units throughout the world. The seven basic units included in it are- mass (kilogram, \[kg\] ), length (metre, \[m\] ), current (ampere, \[A\] ), temperature (kelvin, \[K\] ), time (second, \[s\] ), luminous intensity (candela, \[cd\] ).

Note: According to the second law of motion, force is required to change the state of rest or motion of a body, therefore brakes apply the force required to bring the train to rest. Equations of motion can only be applied when acceleration is constant; this means there are no external forces acting on the system. Equations of motion in a straight line give us the relationship between initial velocity, final velocity, acceleration, distance covered and time taken.