markosheehan Posted October 1, 2016 Share Posted October 1, 2016 A particle travels srating with a initial speed u, with uniform acceleration a. Show that the distance travelled during the nth second is u+an-.5a. I tried working this out by putting this information into the formula S=ut+.5at^2 but it did not work Link to comment Share on other sites More sharing options...
Janus Posted October 1, 2016 Share Posted October 1, 2016 In the formula S = ut+.5at^2 u is the velocity at the beginning of the time interval you are interested in, and t is the duration of the time interval you are interested in. So, with the information given, What would be the new value for u at the start of the nth second, and what is the duration of the nth second? Link to comment Share on other sites More sharing options...
swansont Posted October 1, 2016 Share Posted October 1, 2016 A particle travels srating with a initial speed u, with uniform acceleration a. Show that the distance travelled during the nth second is u+an-.5a. I tried working this out by putting this information into the formula S=ut+.5at^2 but it did not work It should. You need the speed at time t to go into the formula. Link to comment Share on other sites More sharing options...
J.C.MacSwell Posted October 2, 2016 Share Posted October 2, 2016 If you want to use u as described, and use t as n seconds, you need to subtract the distance traveled up to n-1 seconds. Link to comment Share on other sites More sharing options...
Country Boy Posted October 26, 2016 Share Posted October 26, 2016 Yes, S=ut+.5at^2 is the distance traveled in time t- from 0 to t seconds if u is in units of "distance per second" and a is in units of "distance per second per second". The distance traveled "in the nth second" is the distance traveled from 0 up to n seconds minus the distance traveled in n-1 seconds. That is, (un+ .5an^2)- (u(n-1)+ .5a(n- 1)^2)= un+ .5an^2- (un- u+ .5an^2- an+ .5a)= u+ an- .5a since the "un" and ".5an^2" terms cancel. Link to comment Share on other sites More sharing options...
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