Subject: Physics
Topic: 4. Linear kinematics
Sub-Topic: 4.5 Distance travelled in nth second
Question 1: An uniformly accelerated body travels a distance of 24 m in $5^{\text{th}}$ second of its motion and 44 m in $15^{\text{th}}$ 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: $$s_n = u + \frac{1}{2} g(2n-1)$$ $$24 = u + \frac{9a}{2}$$ $$44 = u + \frac{29a}{2}$$ (ii) - (i) gives $$20 = 10a$$ $$a = 2 m/s^2$$
Question 2: A body, starting with some velocity, experiences uniform acceleration. It travels a distance of 20 m in $5^{\text{th}}$ second and 36 m in $9^{\text{th}}$ second. The acceleration of the particle (in $(m/s^2))$ is
1) 4
2) 2
3) 6
4) 8
Hint: $$s_n = u + \frac{1}{2} g(2n-1)$$ $$20 = u + \frac{9a}{2}$$ 36 = u + 17a (ii) - (i) gives 16 = 4a a = 4 m/s2
Question 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: $$s_9 = u + \frac{1}{2}(4)[2(9)-1]$$ $$36 = u + 34$$ $$u = 2 m/s$$
Question 4: A particle starts moving along a straight line with velocity ' $u$ ' and a constant acceleration ' $a$ ', the distance it travels in $15^{\text{th}}$ second is
1) 54 m
2) 58 m
3) 60 m
4) 64 m
Hint: $$s_n = u + \frac{1}{2} g(2n-1) = 2 + [\frac{1}{2} \times 4 \times 29] = 2 + 58 = 60 m$$