Question

Please Help I need Help! Not just mentally but with this math problem!! AHH I am going to go insane. I have had 3 different people help me with this problem and the answers that I got are not the ones that I have to choose from.
An object is moving along a horizontal line on the interval 1 ≤ t ≤ 3, where t is measured in seconds. The object has an initial position x(1) = 3 meters and a velocity of v(t) = 1.5t meters per second. Find the object’s position when t = 3 seconds

Answer 1

Someone told me earlier that it was (1.5)(3)=4.5+3 = 7.5 but that is not the correct answer.

Answer 2

Well v(t) = 1.5t
Therefore the position x(t) can be obtained by integrating v(t).
x(t) = (1.5/2)t^2 + c
x(t) = 0.75t^2 + c

But since we have the coordinates (1,3)
3 = 0.75(1)^2 + c
c = 2.25

x(t) = 0.75t^2 + 2.25
x(3) = 0.75*3^2+ 2.25
x(3) = 9

Answer 3

Thank you so much! I knew I had to integrate something, I just was not sure what.

Answer 4

Yeah, 1.5(3) only applies for constant velocity.
In physics based questions, the velocity is the derivative of the position
And the acceleration is the derivative of the velocity