Aparticle moves in a straight line so that its velocity at time
tis v(t) = t3. if its position at time t is s(t) and
s(1)= 2, find s(2).

s(2) = 7.75

Step-by-step explanation:

given the velocity v(t) = t^3

we can find the position s(t) by simply integrating v(t) and using the boundary conditions s(1)=2

we know throught s(1) = 2, that at t=1, s =2. we can use this to find the value of the constant c.  

Now we can use this value of t to formulate the position function s(t):

this is the position at time t.

to find the position at t=2

the position of the particle at time, t =2 is s(2) = 7.75