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My kids and i had a car accident a month ago. i was driving home after picking them from school. we always take the same route and the traffic that day was moderate. i was driving at a speed of about 40 - 45km/hr before approaching a queue and as i was slowing down or reducing speed coming up to the queue, a car suddenly hit us from the rear end and i ended up hitting the vehicle in front us. there are damages to my vehicle at the rear end and the front. the vehicle i hit had no damages, just a rip to the spare tyre cover. i need to know who is liable for the damages to my vehicle?

If the accident occured exactly as you've described, the rear car would be liable to the damage at the rear of your car, but it doesn't automatically follow that the damage to the front of your car and damage to the car in front (if damaged) is also the responsibility of the driver behind.
It's a common misconception in situations such as this that the rear car is always liable for the damage. However, it's not always possible to determine the sequence of events (ie: who impacted first) and in the event the rear impact occured first, that the rear car pushed you into the front one or whether you would have hit the front car regardless of the rear impact.
So, in summary, it would appear that the rear car is responsible for your rear damage, but it's not clear who is responsible for the front damage.
An insurance company would act on your behalf if you were insured, but due to the nature of the question, I'm assuming you're not insured, hence you may need to fight this out in court yourself.