Can someone please help with this motion question?

A particle is moving in a straight line so that its displacement x cm over time t seconds is given by x = t [square root (49-t^2)].

A) For how many seconds does the particle travel? Answer: 7s

B) How far does the particle move altogether? Answer: 49cm

It's pretty clear from the square root function that t must be strictly less than or equal to 7, and since t cannot be negative, the particle is in motion between t=0 and t=7, hence it is in motion for 7 seconds.

For the second question, we find that:

Sub that value of t back into the original equation, and you'll find the particle travels there and back to the origin for a total of 49cm.

Hey guys, this multi has me stuck i cant work it out. Help is much appreciated. Thanks

As soon as you see an at least question for probability, your mind should instantly think 'how can I use the complement?' ie. (1-P(opposite of situation)).

Here, the complement of at least one movie ticket is going to be no movie tickets. The only way Darren can get no movie tickets is if he doesn't win at all ie. from both prizes, he doesn't win. The chance of this happening is 15/20 * 14/19, since the tickets are implied to not be replaced (and they never are in prize draws anyway.) Therefore, the chance of him winning at least one ticket is 1 minus this value, which is 17/38, hence the answer should be

**D**.