Question

if a cyclist starts at 7 km/hr and he increases his speed in every 3 hours by 1 km/hr then the time taken by the cyclist to cover 113 km is:

Answer 1

Let initial velocity u= 7km/hr

and the speed increases by 1 km/hr in every 3 hr.

Hence acceleration a = 1/3 $\frac{km}{hr^{2} }$

Now we have total distance covered S= 113km.

Now using kinematic equation i.e. S= ut+$\frac{1}{2}$a$t^{2}$, we get

113=7t+$\frac{1}{2}$$\frac{1}{3}$$t^{2}$

i.e. $\frac{1}{2}$$\frac{1}{3}$$t^{2}$+7t-113=0

Multiplying by 6 on both sides we get,

$t^{2}$+42t-678=0

so after solving this polynomial equation we get two roots

i.e t=-21-$\sqrt{1119}$ and t=$\sqrt{1119}$-21

but as we know time is never negative.

so the time required for cyclist to travel 113 km distance is $\sqrt{1119}$-21 hr.