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fredd
10 hours ago
10

The position of a particle is r⃗ (t)=(3.0t2iˆ+5.0jˆ−6.0tkˆ)m. (a) Determine its velocity and acceleration as functions of time.

(b) What are its velocity and acceleration at time t = 0?
Physics
1 answer:
ValentinkaMS [1.1K]9 hours ago
8 0

Explanation:

It is stated that,

The position of a particle is defined by:

r(t)=(3t^2i+5j-6tk)\ m

(a) The velocity of a particle can be expressed as:

v=\dfrac{dr(t)}{dt}

Substituting the values,

v=\dfrac{d}{dt}(3t^2+5-6t)\\\\v=(6ti-6k)\ m/s

The acceleration of the particle can be expressed as:

a=\dfrac{dv}{dt}\\\\a=\dfrac{d}{dt}(6t-6)\\\\a=6i\ m/s^2

(b) At time t = 0,

Velocity, v = 6k m/s

Acceleration, a = 6i m/s²

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