A truck starts from rest with an acceleration of 1.5 metre/sec² while a car 150 metre behind starts from rest with an acceleration of 2 metre/sec². How long will it take before both the truck and car to be side by side, and how much distance is travelled by each?

Let x be the distance travelled by the truck when both truck and car are side by side. The distance travelled by the car will be (x + 150) as the car is 150 metre behind the truck. Applying the formula
$\text{s=ut+}\left(\text{1/2}\right){\text{a\hspace{0.17em}\hspace{0.17em}t}}^{\text{2}}\text{,}$  we have
$\text{x=1/2}\times \left(1.5\right)t^2\mathrm{..........}\left(1\right)$
$and(x+150)=(1/2)\times \left(2\right)t^2\mathrm{..........}\left(2\right)$
Here t is the common time.
From eqs. (1) and (2) we have
$=\frac{x+150}{x}=\frac{2}{1.5}$
Solving we get  $x=450$ metre (truck) and  $x+150=600$ metre (car).
Substituting the value of x in eq. (1),
We get  $450=1/2\left(1.5\right)t^2$
$\therefore t=\sqrt{\frac{450\times 2}{1.5}}=\sqrt{600}=24.5\sec .$