A particle is moving in a straight line under constant acceleration. It travels `15 m` in the `3^(rd)` second and `31 m` in the `7^(th)` second. Find the initial velocity and constant acceleration.

Explanation

Displacement is `15 m` in the `3^(rd)` second and `31 m` in the `7^(th)` second.
Displscement in the `t^(th)` second
`s_(t)=u+1/2a(2t-1)`
For the `3^(rd)` second, `s_(t)=15 m`
`15=u+1/2a(2xx3-1)=u+(5a)/2 …(i)`
For the `7^(th)` second, `s_(t)=31m`
`31=u+1/2a(2xx7-1)=u+(13a)/2 ...(ii)`
Solving (i) and (ii), we get
`u=5 m//s, a=4m//s^(2)`