Final answer:
The object moves with uniform accelerated motion and decelerates as time progresses, with an initial positive position reducing over time. Its velocity is negative and increasingly so, and it has a constant negative acceleration.
Step-by-step explanation:
The nature of the object's motion can be deduced by analyzing its position function, x=40−t². This is a quadratic equation where the coefficient of the t² term is negative, indicating that the position x decreases as time t increases. The motion described is uniform accelerated motion, with the object decelerating as time progresses. If we consider the velocity as the derivative of the position, we can find that v(t) = dx/dt = -2t. This shows that the velocity is indeed changing with time, confirming the object is accelerating (or decelerating, in this case).
The object starts from x=40 when t=0 and moves towards the origin as time increases. At t=√40, the object would cross the x-axis, this is the time when the position x becomes zero. The acceleration can be found by taking the second derivative of the position function, which yields a(t) = -2, a constant, showing uniform acceleration. In summary, the object has an initial positive position, moves toward the origin with increasing negative velocity, and has a constant negative acceleration.