Question:
Obtain a relation for the distance travelled by an object moving with a uniform acceleration in the interval between 4 th and 5 th seconds.
Solution:
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
$=\mathrm{S}_{5}-\mathrm{S}_{4}$
$=5 u+\frac{25}{2} a-4 u-8 a=u+\frac{9}{2} a$