Question

A body moving with uniform acceleration travels a distance of sn=(0.4n+9.8) m in nth second. find the initial velocity of the body

Answer 1

Final Answer: $10m/s$

Steps:
1) Given,
$S_n = 0.4n + 9.8$

We know for uniform acceleration,
Displacement in 'nth' second is given by :
$S_n = u + \frac{1}{2}a(2n-1) \\ => 0.4n + 9.8 = u + an -a/2 \\ => 0.4 n + 9.8 = an + u-a/2$

Here, S_n will always be in given form in uniform acceleration where coefficient of n is acceleration .
Comparing :
$a = 0.4m/s^2 \\ and \\ u-a/2 = 9.8 \\ =>u-0.2 = 9.8 \\ => u = 10m/s$

Hence, Initial velocity is 10m/s .