Obtain a relation for the distance travelled

We know, distance travelled by a uniformly accelerated object in time t is given by

$\mathrm{S}=u t+\frac{1}{2} a t^{2}$

Distance travelled after 4 th second.

$\mathrm{S}_{4}=4 u+8 a$

Distance travelled after 5 th second,

$S_{5}=5 u+\frac{25}{2} a$

$\therefore$ Distance travelled between 4 th and 5 th seconds

$=\mathrm{S}_{5}-\mathrm{S}_{4}$

$=5 u+\frac{25}{2} a-4 u-8 a=u+\frac{9}{2} a$