If the position vector of an object is r(t)=4ti-3j, what are the instantaneous velocity vector components at t=1s?

To determine the instantaneous velocity vector components from the position vector r(t) = 4ti - 3j, we first need to find the derivative of the position vector with respect to time, t. The velocity vector v(t) is given by the formula v(t) = dr/dt.

Taking the derivative:

1. The component along the i direction (x-direction) is derived from the term 4t. The derivative of 4t with respect to t is 4, meaning the x-component of the velocity is consistently 4 m/s.

2. The j component (y-direction) comes from the term -3, which is a constant, and thus its derivative is 0. This tells us that the y-component of the velocity is 0 m/s.

Consequently, at any time, including at t = 1s, the instantaneous velocity vector components are vx = 4 m/s and vy = 0 m/s.

This matches option C, confirming it as the correct answer. The consistent nature of the x-component suggests a steady movement in that direction, while the lack of change in the y-component indicates no movement vertically.