After a boulder is pushed down a hill, its speed s(t) at time t is given by the formula s(t)=v+at, where v is the initial velocity and a is the acceleration. If s(2)=16 and s(5)=25, find the initial velocity and acceleration.(round to the nearest tenth)

Answer 1

acceleration: a
v(t) = at + c
it says it was pushed, so we may assume initial velocity is zero, thus
0 = a(0) + c ---> c=0
v(t) = at
s(t) = (1/2)at^2 + k

given: when t=2, s(2) = 16
(1/2)a(4) + k = 16
2a + k = 16 ****

when t=5, s(5) = 25
(1/2)a(25) + k = 25
(25/2)a + k = 25 ***
subtract equations marked ***
(21/2)a = 9
a = 18/21 = 6/7
in 2a + k = 16
12/7 + k = 16
k = 100/7

initial velocity is 0
a = 6/7