Question

A car $A$ is travelling along a straight level road with a uniform speed of $60km/hr$ It is followed by another car $B$ which is travelling uniformly at $70km/h$ When the distance between them is $2km$ , the car $B$ decelerates at $20km/h^2$ Where will $B$ catch up with $A$ ?

Answer 1

For B to catch A both will have to reach the same point in same time.

Let that distance be $x$ . B will have to cover $x+2km$in the same time.

For B equation will be

$x=60km/hr\times t$

$t=\frac{x}{60}hr$

For A equation will be

$x+2=70km/hr\times \frac{x}{60}hr+\frac{1}{2}\times -20km/h{r}^2\times {\left(\frac{x}{60}\right)}^2$

$x^2-60x+720=0$

The solution for the above equation using the quadratic formula will be

$x=30\left(1\pm \sqrt{2}\right)km$

As we have to find the shortest distance, that distance will be

$x=30\left(1-\sqrt{2}\right)km$