A particle starts to move in a straight line from a point with velocity 10 m/s and acceleration - 20 m/s²? Find the position and velocity of the
particle at (i) t = 5s, (ii) t' = 10 s.

s(5) = -200,  v(5) = -90

              s(10) = -900, v(10) = -190

Explanation:

Position: s(t)

Velocity:  s'(t) = v(t)                ⇒      

Acceleration     v'(t) = a(t)      ⇒      

We are given that acceleration a(t) = -20   and velocity v(t) = 10

(a) Input t = 5 into the s(t) and v(t) equations

   s(5) = -10(5)² + 10(5)           v(5) = -20(5) + 10

          =  -250  +  50                     = -100   +  10

          =       -200                          =        -90

(b) Input t = 10 into the s(t) and v(t) equations

     s(10) = -10(10)² + 10(10)           v(10) = -20(10) + 10

            =  -1000  +  100                     = -200   +  10

            =       -900                          =        -190

the ima (higher than 1m) will be greater than the ima with the height of 1m.