The velocity time graphs of a car and a scooter are shown in the figure. (i) The difference between the…

Distance travelled by car in $15 \mathrm{s}$ $=\frac{1}{2}\times 45\times 15\times =\frac{675}{2} \mathrm{m}$. Distance travelled by scooter in $15 \mathrm{s}$$=30 \times 15=450$. Let car catches scooter in time $t$
difference between the distance travelled by car and scooter in $15 \mathrm{s}$ in$\text{⇒\hspace{0.17em}}450-\frac{675}{2}=112.5\mathrm{m}$
$\Rightarrow \frac{675}{2}+45\left(t-15\right)=30t$
$337.5+45t-675=30t \Rightarrow 15 t=337.5$
$\Rightarrow t=22.5 \mathrm{s}$.