J J Science Academy - Test Paper

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) $(1 \mathrm{~m} / \mathrm{s}^{2})$

2) $(2 \mathrm{~m} / \mathrm{s}^{2})$

3) $(4 \mathrm{~m} / \mathrm{s}^{2})$

4) $(0.5 \mathrm{~m} / \mathrm{s}^{2})$

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 $(5^{\text {th }})$ second and 36 m in $(9^{\text {th }})$ second. The acceleration of the particle (in $(\mathrm{m} / \mathrm{s}^{2})$ ) 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

3) A particle starts moving along a straight line with velocity ' $(u)$ ' and a constant acceleration ' $(a)$ ', the initial velocity is

1) $(1 \mathrm{~m} / \mathrm{s})$

2) $(-1 \mathrm{~m} / \mathrm{s})$

3) $(2 \mathrm{~m} / \mathrm{s})$

4) $(-2 \mathrm{~m} / \mathrm{s})$

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 $(15^{\text {th }})$ second is

1) 54 m

2) 58 m

3) 60 m

4) 64 m

Hint: $$s_n=u+\frac{1}{2} g(2n-1)=2+\left[\frac{1}{2} \times 4 \times 29\right]=2+58=60 m$$