Final answer:
The velocity of the cart at t=3 seconds is calculated using the kinematic equation for velocity, yielding a result of 3 m/s in the positive x-direction.
Step-by-step explanation:
The question involves finding the velocity of a cart at a certain time given its initial position, velocity, and constant acceleration. To find the velocity of the cart at t=3 seconds (t=3s), we can use the kinematic equation for velocity:
v = v0 + at,
where v is the final velocity, v0 is the initial velocity, a is the constant acceleration, and t is the time.
Here, the initial velocity v0 = -6 m/s (since it's in the negative x-direction), the acceleration a = 3 m/s2 (in the positive x-direction), and the time t = 3 s.
Substituting the values into the equation:
v = (-6 m/s) + (3 m/s2)(3 s) = -6 m/s + 9 m/s = 3 m/s.
The velocity of the cart at t=3s is 3 m/s in the positive x-direction.