A particle starting from initial velocity v_0 moves on straight line with constant acceleration equation of distance travelled during n^"th" second will be …... .

A particle starting from initial velocity v_0 moves on straight line w

1.	A particle starting from initial velocity v_0 moves on straight line with constant acceleration equation of distance travelled during n^"th" second will be …... .
Answer» SOLUTION :For given particle, DISTANCE TRAVELLED in `n^(th)` seconde is, d = (distance travelled in n seconds) - (distance travelled in (n-1) second) `= (v_(0) n + 1//2 an ^(2)) -(v_(0) (n -1) +1/2 a (n-1) ^(2))` (From equation `d = v _(0) t + 1/2 at ^(2))` `=( v _(0) n + 1/2 an ^(2)) - (v _(0) n - v_(0) + a//2 (n ^(2) -2n +1))` `=(v_(0) n + 1/2an ^(2) -v _(0) n + v_(0) -1/2 an ^(2) + an - (a)/(2))` `= v _(0) + a _(n) - (a)/(2)` `therefore d = v _(0) + a/2 (2n -1)`