The chart below represents the kinematics of a freely falling body. Time
(seconds t) Total Distance meters d (t)
1 5
2 20
3 45
4 80
5 125
a. Is the relationship between time and distance an arithmetic sequence? Explain.

b. The total distance a freely falling body covers in time, t, is given by the equation d(t)=1/2 gt2, where g is constant at 10 m/s2.

c. Show, in terms of n, the distance a falling body covers in t = n - 1 seconds of movement.

d. The distance a freely falling body covers in the nth second is given by s(n)=d(n)-d(n-1). Show s(n) in terms of g, in simplified form.

e. Prove that the quantities s(n) form an arithmetic sequence.