v = v_0 + a*t
x = v_0 * t + a * t^2/2
"Now fill in what we know :"
10 = v_{01} * 5 + a * 5^2/2
10 = v_{02} * 3 + a * 3^2/2
v_{02} = v_{01} + a*5
=> 10 = v_{01} * 3 + a * 5 * 3 + a * 3^2/2
=> 10 = 3 * v_{01} + 19.5 * a
"Now we have a system of two linear equations in 2 variables"
v_{01} " and "a.
5 v_{01} + 12.5 a = 10
3 v_{01} + 19.5 a = 10
"Subtract the second equation from the first :"
2 v_{01} - 7 a = 0
=> v_{01} = 3.5 a
=> 10.5 a + 19.5 a = 30 a = 10
=> a = 1/3 "m/s²"
=> v_{01} = 7/6 "m/s"
"Next 2 seconds : "
v_0 = v_{03} = v_{02} + a*3 = v_{01} + a*8 = 7/6 + 8/3 = 23/6
=> x = (23/6) * 2 + (1/3) * 2^2 / 2 = 23/3 + 2/3 = 25/3 = 8.333