A toy car initially moving with a uniform velocity of 18 km h^-1 comes to a stop in 2 s. Find the retardation of the car in S.I. units.

As we know,

$\text {a} = \dfrac {\text {final vel. (v)} - \text {initial vel. (u)}}{\text {time (t)}}$

Given,

Initial velocity (u) = 18 km h^-1

To convert initial velocity u to m s^-1

$18 \text { km h}^{-1} = \dfrac{18 \text { km}}{1 \text{ h}} = \dfrac {18 \times 1000 \text{ m}}{60 \times 60 \text{ s}} \\[0.5em] \Rightarrow 18 \text { km h}^{-1} = \dfrac {18 \times 10 \text{ m}}{6 \times 6 \text{ s}} \\[0.5em] \Rightarrow 18 \text { km h}^{-1} = 5 \text{ m s}^{-1} \\[0.5em]$

Hence, 18 km h^-1 is equal to 5 m s^-1.

Final velocity (v) = 0

Time (t) = 2 s

Substituting the values in the formula above, we get,

$\text {Acceleration (a)} = \dfrac {0 - 5}{2} \\[0.5em] \text {Acceleration (a)} = -\dfrac {5\text { ms}^{-1}}{2\text { s}} \\[0.5em] \Rightarrow \text {Acceleration (a)} = - 2.5 \text { ms}^{-2} \\[0.5em]$

Hence, acceleration of the body is -2.5 m s ^-2. Negative sign shows that the velocity decreases with time, so retardation is 2.5 m s ^-2.