For an object moving with uniform acceleration, travelling 50m in 5th sec, 70m in 7th sec

a)Its initial velocity is $5m/s$

b)Its acceleration is $20m/s^2$

c)Its travels 100m in $9^{th} sec$

d) Its average velocity during$9^{th} sec is 90m/s$

Given that for a body moving with uniform acceleration

Initial velocity = u, acceleration = a

$$\begin{gathered} s_5=50m , s_7=70m \\ We get S_5=u+a\left(5-\frac{1}{2}\right)=50\Rightarrow u+\frac{9a}{2}=50 \\ {S}_7=u+a\left(7-\frac{1}{2}\right)=70 \\ u+6.5a=70 \\ \_u\pm 4.5a=\_50 \\ \_\_\_\_\_\_\_\_\_\_\_\_\_ \\ 2a=20 \\ a=10m{s}^{-2} \\ u=5m/s \\ Calculate dis\tan ce travel in 9^{th} second \\ {S}_9=u+a\left(9-\frac{1}{2}\right) \\ {S}_9=5+10\left(\frac{17}{2}\right) \\ {S}_9=90m \\ Let final velocity after 8 sec \\ v=u+at=5+8\times 10=85 m/s \\ (means during 9^{th} second) \\ And final velocity after 9 seconds \\ v=u+at \\ =5+10\times 9 \\ =95 m/s \\ so {\overrightarrow{v}}_{Avg}=\frac{85+95}{2}=90m/s during 9^{th} second of journey \end{gathered}$$