First slide

Position Path Length (Distance) And Displacement

Question

A body starts from rest with uniform acceleration. If its velocity after n second is v, then its displacement in the last two seconds is

Easy

A

$\frac{2 V (n - 1)}{n}$
B

$\frac{V (n - 1)}{n}$
C

$\frac{V (n + 1)}{n}$
D

$\frac{2 v (2 n + 1)}{n}$

Solution

Using v - u + at, we have
v= a n or a = v/n
Now $s (n) = \frac{1}{2} (\frac{V}{n}) n^{2}$
and $s (n - 2) = \frac{1}{2} (\frac{V}{n}) (n - 2)^{2}$
so, the distance travelled in last two seconds is
$s (n) - s (n - 2) = \frac{2 v (n - 1)}{n}$

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