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: $$s_n = u + \frac{1}{2} g(2n-1)$$$$24 = u + \frac{9 a}{2}$$$$44 = u + \frac{29 a}{2}$$(ii) - (i) gives$$20 = 10 a$$$$a = 2 m / s^2$$
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 $(m / s^2)$ is
1) 4
2) 2
3) 6
4) 8
Hint: $$s_n = u + \frac{1}{2} g(2n-1)$$$$20 = u + \frac{9 a}{2}$$36 = u + 17a(ii) - (i) gives16=4aa = 4 m/s2
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: $$s_n = u + \frac{1}{2} g(2n-1) = 2 + [\frac{1}{2} \times 4 \times 29] = 2 + 58 = 60 m$$