1)
An uniformly accelerated body travels a distance of 24 m in $5^{th}$ second of its motion and 44 m in $15^{th}$ sec of its motion. The acceleration of the particle will be
Hint:
$$s_n=u+\frac{1}{2} g(2n-1)$$
$$24=u+\frac{9a}{2}$$
$$44=u+\frac{29a}{2}$$
(ii) - (i) gives
$$20=10a$$
$$a=2 m / s^2$$
2)
A body, starting with some velocity, experiences uniform acceleration. It travels a distance of 20 m in $5^{th}$ second and 36 m in $9^{th}$ second. The acceleration of the particle (in $m / s^2$) is
Hint:
$$s_n=u+\frac{1}{2} g(2n-1)$$
$$20=u+\frac{9a}{2}$$
$$36 = u + 17a$$
(ii) - (i) gives
$$16=4a$$
$$a = 4 m/s^2$$
3)
A particle starts moving along a straight line with velocity '$u$' and a constant acceleration '$a$', the initial velocity is
Hint:
$$s_9=u+\frac{1}{2}(4)[2(9)-1]$$
$$36=u+34$$
$$u=2 m / s$$
4)
A particle starts moving along a straight line with velocity '$u$' and a constant acceleration '$a$', the distance it travels in $15^{th}$ second is
Hint:
$$s_n=u+\frac{1}{2} g(2n-1)=2+\left[\frac{1}{2} \times 4 \times 29\right]=2+58=60 m$$