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
1) $1 m/s^{2}$
2) $2 m/s^{2}$
3) $4 m/s^{2}$
4) $0.5 m/s^{2}$
Hint: $$s_n=u+\frac{1}{2} g(2n-1)$$$$24=u+\frac{9a}{2}$$... (i)$$44=u+\frac{29a}{2}$$(ii)(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: $$s_n=u+\frac{1}{2} g(2n-1)$$$$20=u+\frac{9a}{2}$$... (i)$$36 = u + 17a$$(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
1) $1 m/s$
2) $-1 m/s$
3) $2 m/s$
4) $-2 m/s$
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
1) 54 m
2) 58 m
3) 60 m
4) 64 m
Hint: $$s_{n}=u+\frac{1}{2} g(2n-1)=2+\left[\frac{1}{2} \times 4 \times 29\right]=2+58=60 m$$