A particle starting from rest moves with constant acceleration.

Question:

A particle starting from rest moves with constant acceleration. If it takes $5.0$ s to reach the speed $18.0$ $\mathrm{km} / \mathrm{h}$

Find

(a) The average velocity during this period

(b) The distance travelled by the particle during this period.

Solution:

$\mathrm{u}=0 ; \mathrm{t}=5 \mathrm{sec} ; \mathrm{v}=18 \times 5 / 18=5 \mathrm{~m} / \mathrm{s}$

$\mathrm{v}=\mathrm{u}+\mathrm{at}$

$5=0+a(5)$

$a=1 \mathrm{~m} / \mathrm{s}^{2}$

$S=u t^{\frac{1}{2}} a t^{2}$

$\mathrm{S}=0+\frac{\frac{1}{2}}{2}(\mathrm{a})(5)^{2}$

$\mathrm{S}=12.5 \mathrm{~m}$

$\mathrm{V}_{\mathrm{avg}}=$ distance/time $=\frac{12.5}{5}$

$V_{a v g}=2.5 \mathrm{~m} / \mathrm{s}$

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