Question

a body moving with uniform acceleration travels a distance Sn=(0.4n+9.8)m in nth sec. find the initial velocity of the body in ms-1?

Answer 1

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Answer on Question #47321, Physics, Mechanics | Kinematics | Dynamics

Question:

A body moving with uniform acceleration travels a distance $S_n = (0.4n + 9.8)m$ in nth sec. find the initial velocity of the body in ms-1?

Answer:

Distance covered during $n^{\text{th}}$ second equals:

$$S_n = \left(v_0 t_n + \frac{a t_n^2}{2}\right) - \left(v_0 t_{n-1} + \frac{a t_{n-1}^2}{2}\right)$$

where

$$t_n = 1s \cdot n, \quad t_{n-1} = 1s \cdot (n - 1)$$

Therefore:

$$S_n = v_0 \cdot 1s + a \cdot n \cdot (1s)^2 - \frac{a(1s)^2}{2} = \left(v_0 - \frac{a}{2}\right) + an$$

Comparing with $S_n = (0.4n + 9.8)$

$$a = 0.4$$ $$v_0 = \frac{a}{2} + 9.8 = 10 \frac{m}{s}$$

Answer: $10 \, \text{m/s}$