If u(t) = 6t 1.9 m/s and s = 2 m when t 0, find expressions for a(t) and s(t). calculate values for s(t), v(t), and a(t) for times t = 0, 1, 2, and 3 seconds and tabulate the results.

t   in s                   0                    1                    2                    3

-------------------------------------------------------------------------------------------

s  in m                  2                  4.068          17.44              55.05

a  in m/s²             0                    11.4            21.27             30.64

--------------------------------------------------------------------------------------------

Explanation:

Given:

u(t) =

s = 2 m at t = 0

Now,

u(t) =

thus,

or

on integrating, we get

or

s =

here c is the integration constant

s =

now, at t = 0, s = 2 m

thus,

2 =

or

c = 2

hence,

the expression is

s =

also,

a(t) =

or

a(t) =  

or

a(t) =  

or

a(t) =

now,

at t = 0

s =  

or

s = 2 m

and,

a =

or

a = 0 m/s²

at t = 1

s =  

or

s = 4.068 m

and,

a =

or

a = 11.4 m/s²

at t = 2

s =  

or

s = 17.44 m

and,

a =

or

a = 21.27 m/s²

at t = 3

s =  

or

s = 55.05 m

and,

a =

or

a = 30.64 m/s²

t   in s                   0                    1                    2                    3

-------------------------------------------------------------------------------------------

s  in m                  2                  4.068          17.44              55.05

a  in m/s²             0                    11.4            21.27             30.64

--------------------------------------------------------------------------------------------