Question

calculate initial velocity and acceleration of particle travelling with uniform acceleration in a straight line if it travels 55 m in the 8th second and 85 m in the 13th second of its motion

Answer 1

equation for distance travelled in one second in uniform acceleration is
$s=u+a(2n-1)/2$
 u-intial velocity
 a-acceleration
55=u+a/2(2*8-1)=u+7.5a.....(1)
similarly 85=u+12.5a.....(2)
(2)-(1)
5a=30  
a= 6 m s⁻²
therefore u=55-7.5(6)=55-45=10 m s⁻¹