An object's velocity in m/s is given by the equation vx (t) = 10t-2. If it starts at x=0 at t=0, what is its position after 5 seconds?

Answer: d (5) = 115m

Position after 5 seconds is 115m

Explanation:

Given;

Initial position d (0) = 0

Time = 5 sec

Velocity function vx (t) = 10t - 2

To determine its position after 5 sec we need to calculate the position function.

d (t) = integral of vx (t)

d (t) = ∫10t - 2

d (t) = (10/2) t^2 - 2t + c

d (t) = 5t^2 - 2t + d (0)

c = d (0) = 0

d (t) = 5t^2 - 2t

So, at time t = 5

d (5) = 5 (5^2) - 2 (5) = 125 - 10

d (5) = 115m