A train starts from rest and moved with a constant acceleration of

Solution:

$A=$ slope $=\frac{v}{t}$

$2=\frac{v}{30}$

$\mathrm{v}=60 \mathrm{~m} / \mathrm{s}$

(a) Distance $=$ Area of $v-t$ graph

$=\frac{1}{2}(30+60)(50)$

$=2700 \mathrm{~m}$

$=2.7 \mathrm{~km}$

(b) Maximum speed

$\mathrm{V}=60 \mathrm{~m} / \mathrm{s}$

Velocity $30 \mathrm{~m} / \mathrm{s}$ is achieved at $\mathrm{t}=15 \mathrm{sec}$ and $\mathrm{t}=60 \mathrm{sec}$ Area of (v-t) graph in first 15 second

$\mathrm{s}=\frac{\frac{1}{2}}{2}(15)(30)=225 \mathrm{~m}$

Area of (v-t) graph in first $60 \mathrm{sec}$

$S=\frac{1}{2} \times 30 \times 60+\frac{1}{2}(60+30)(3)$

$=2250 \mathrm{~m}$

$=2.25 \mathrm{~km}$