The velocity of an object at time t is given by v(t)=9t^2 8t - 10.

Question

At time t=1, the position of the object is S(1)=1. How many and which ones are true? :

S(0)=4

S(2)=24

S(3)=91

Answer 1

I assume you mean the velocity is given by  v(t) = 9t^2 + 8t - 10

(missing a plus sign)

All three are true.  Integrate the velocity function to get the position.

S(t) =3t^3 + 4t^2 - 10t + c

where c will equal 4 due to the initial condition given.

Then plug in for t and decide whether they are true.  I assume my math was correct.

Answer 2

I also assume v(t) = 9t^(2) + 8t - 10, then you can integrate it (and not differentiate it like Boiler said) to find s(t). I got s(t) = 3t^3 + 4t^2 - 10t + C

then you use your the initial conditions given ( s(1) =1) ):

s(1) = 1 = 3(1)^3 + 4(1)^2 - 10(1) + C

1 = 3 + 4 - 10 + C

C = 4

So, s(t) = 3t^3 + 4t^2 - 10t + 4.

Now you check which ones are true by plugging your different times in the position versus time equation s(t):

t = 0: s(0) = 4  It's true.

t = 2: s(2) = 24  It's true also.

t = 3: s(3) = 91  And again it's true!