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A particle moves with an acceleration a = 2i - j m/s^2. For t = 0 s the particle is at the point (0,0) with a velocity vo = i + 2j m/s. Calculate the average velocity with which the particle has moved in the time interval of 5 s.

Sagot :

nengikim

Answer:

We can find the average velocity of the particle by following these steps:

* Find the particle's final velocity (v(t)): We can achieve this by integrating the acceleration (a) with respect to time (t). Since acceleration is the rate of change of velocity, integrating it will give us the velocity function.

* Average velocity: Once we have the final velocity (v(5)), we can calculate the average velocity by averaging the initial velocity (vo) and the final velocity (v(5)).

Calculation:

* Finding final velocity (v(t)):

v(t) = ∫ a(t) dt = (2t - t)i + (-t)j = ti + (-t)j

* Average velocity:

Average velocity = (vo + v(5)) / 2

= ((1i + 2j) + (5i - 5j)) / 2

= (6i - 3j) / 2

= 3i - 1.5j m/s

Therefore, the average velocity of the particle in the time interval of 5 seconds is 3i - 1.5j m/s.

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