Variable acceleration question

A particle moves in a straight line. At time t seconds after it begins its motion, the acceleration of the particle is 3sqrt(t) where t>0.
Given that after 1 second the particle is moving with a velocity of 2m/s, find the time taken for the particle to travel 16m.

What have you tried?

I've got s=4/5 t^5/2 + c but don't know what to do with that.

I've got s=4/5 t^5/2 + c but don't know what to do with that.

So how did you use the information that v = 2 when t = 1?

If you assume s = 0 when t = 0 then you have c and then you can plug in 16 as s because you know the particle is travelling in a straight line without changing direction - this means that distance traveled = displacement.

Ahh sorry my bad. I didn't realise it said the time taken to TRAVEL 16m. I thought 16m was the displacement.

It is the displacement. It's both.

But how do we know it starts at origin?

"At time t seconds after it begins its motion"

So at t = 0, it is at the "origin".

But you can fix the origin anywhere you like as long as your maths is correct. E.g. you could say that s=2 when t=0 and then find t when s=18.