A motor bike running at $90 \,km h ^{-1}$, is slowed down to $54 \,km h^{-1}$ by the application of brakes, over a distance of $40\, m$. If the brakes are applied with the same force, calculate $(i)$ total time in which bike comes to rest $(ii)$ total distance travelled by bike.
A motor bike running at $90 \,km h ^{-1}$, is slowed down to $54 \,km h^{-1}$ by the application of brakes, over a distance of $40\, m$. If the brakes are applied with the same force, calculate $(i)$ total time in which bike comes to rest $(ii)$ total distance travelled by bike.
Case $1$ : $u=90 km h ^{-1}=(-) 25 ms ^{-1} ; v=54 km$
$h^{-1}=15 m \cdot s ^{-1} ; S =40 m ; a=?$
Applying $v^{2}-u^{2}=2 a S$
$(15)^{2}-(25)^{2}=2 \times a \times 40$
$80 a=-400$
$a=-5 m s ^{-2}$
Case $2$ : $u=90 km h ^{-1}=25 m s ^{-1} ; v=0 ; S =?$
$a=-5 m s ^{-2} ; t=?$
Applying $v^{2}-u^{2}=2 a S$
$(0)^{2}-(25)^{2}=2 \times(-5) \times S$
$S=\frac{-625}{-10}=62.5 m$
Applying $\quad v=u+a t$
$0=25-5 \times t$
or $5 t=25$ or $t=5 s$
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