Question

If a train travelling at 72 km/h is to be brought to rest at a distance of 200 m then its retardation should be :
A. $20m{{s}^{-2}}$
B. $2m{{s}^{-2}}$
C. $10m{{s}^{-2}}$
D. $1m{{s}^{-2}}$

Answer 1

Hint:The rate of change of an object's velocity with respect to time is called acceleration in mechanics. Accelerations are values that are measured in vectors (in that they have magnitude and direction). The orientation of the net force applied on an item determines the orientation of its acceleration. Newton's Second Law describes the magnitude of an object's acceleration as the combined impact of two sources.

Complete step by step solution:
The act or consequence of delaying anything; the amount to which something is slowed or delayed; that which retards or delays. Acceleration in the opposite direction of velocity is always referred to as deceleration. Deceleration usually slows you down. Negative acceleration, on the other hand, is acceleration in the opposite direction in the coordinate system of choice.
Equations of motion are physics equations that describe a physical system's behaviour in terms of its motion as a function of time. More specifically, equations of motion are a collection of mathematical functions that explain the behaviour of a physical system in terms of dynamic variables. Typically, these variables are geographical coordinates and time, but they may also incorporate momentum components.
Here the equation we use is $\mathrm{v}^{2}=\mathrm{u}^{2}+2 \mathrm{as}$
Upon converting km to m and hr to sec
$\mathrm{u}=72 \dfrac{\mathrm{km}}{\mathrm{h}}=72 \times \dfrac{5}{18}=20 \mathrm{~m} / \mathrm{s}$
Now $\mathrm{v}^{2}=\mathrm{u}^{2}+2 \mathrm{as}$
$0=(20)^{2}+2 \mathrm{a}(200)$
$0=400+400 \mathrm{a}$
$400 \mathrm{a}=-400$
Retardation $=-\mathrm{a}=1 \mathrm{~m} / \mathrm{s}^{2}$
$\Rightarrow -a=1m{{s}^{-2}}$
Therefore the correct option is $\left( D \right)$ .

Note:
Acceleration in the opposite direction of velocity is always referred to as deceleration and always comes with a negative sign with it. Negative acceleration, on the other hand, is acceleration in the opposite direction in the coordinate system of choice. Negative acceleration can be confused with slowdown, while deceleration can also be confused with negative acceleration.