Answer:
Velocity = dr/dt = (9.60 i + 0 j - 2.00 · t k) m/s
Acceleration = dv/dt = (0 i + 0 j - 2.00 k) m/s²
Explanation:
Hi there!
The velocity of an object is the variation of the object´s position over time. Then, the velocity can be expressed as the derivative of the position function:
v = dr / dt
Where
v = velocity
dr/dt = variation of the position over time
In this case, we have an object moving in a three-dimension system, that is, the direction of the moving object has an x, y, and z-component.
To obtain the components of the velocity vector, we have to derivate the components of the position vector with respect to time:
r = (9.60 · t i + 8.85 j - 1.00 · t² k)m
v = dr/dt = (9.60 i + 0 j - 2.00 · t k) m/s
The acceleration is the variation of velocity over time, then:
dv/dt = acceleration.
In this case, we have to derivate the velocity vector to obtain the acceleration vector:
a = dv/dt = (0 i + 0 j - 2.00 k) m/s²
The object is only accelerated in the z-direction and the acceleration is constant (-2 m/s²).
