Question

Suppose a particle is at position 3 on a straight line. The Velocity is given by the equation v=2t+1 where velocity is mph and t is hours. The particle beings to move for 3 hours
1) How many miles did the particle move?
2) Draw the geometry for the problem
3) What position is the particle now?

Answer 1

If you're given velocity, to find position, you need to integrate this function given to find position at \(t\)

Answer 2

Alright , but is there any way you can further explain it , it would be really helpful for me~

Answer 3

integrating the function we get \[s(t)= t^2+t+3\]
to find the distance you should find where does the object moves forward and backward by evaluating v(t)=0 and will see that for positive (real) t the object moves forward so we say that d= s(3)-s(0)=3^2+3+1-1= 12miles

Answer 4

I think the position of the particle is just evaluate s(3)= 15

Answer 5

I am sorry about the distance, it's 12 but instead of 1-1 make it 3-3