distance traveled

Question

the table lists the distance traveled by a falling object where  t  is elapsed time in seconds and d  is distance in meters.

  t:  0      1      2        3         4        5                                                       d:  0   4.9    19.6  44.1  78.4  122.5                                             if the distance is modeled by d(t)=at^2  find thd distance traveled after 11 seconds.

Answer 1

From the given table, we can see that a= 4.9 m/s² ---> d(t) = 4.9t² ---> d(11) = 4.9 · 11² ---> d = 592.9 meters

[If there no table is given we can find "a" from the formula of free fall h(t) = (gt²)/2 , g ≈ 9.8 m/s² , a = g/2]