Which of the given relations are true for any arbitrary motion in space?

(a) $$v_{average} = \left (d\frac{1}{2} \right )\left ( v\left ( t_{1} \right ) + v\left ( t_{2} \right ) \right )$$

(b) $$v_{average} = \dfrac{\left [ r\left ( t_{2} \right ) – r\left ( t_{1} \right )\right ]}{\left ( t_{2} – t_{1}\right )}$$

(c) $$v(t) = v\left ( 0 \right ) + at$$

(d) $$r(t) = r(0) + v(0)t + \left (\dfrac{1}{2} \right )at^{2}$$

(e) $$a_{average} = \dfrac{\left [ v\left ( t_{2} \right ) – v\left ( t_{1} \right )\right ]}{\left ( t_{2} – t_{1}\right )}$$

Asked by Abhisek | 1 year ago |  65

##### Solution :-

Explanation:-

It is given that the motion of the particle is arbitrary. Therefore, the average velocity of the particle cannot be given by this equation.

Explanation:-

The arbitrary motion of the particle can be represented by this equation.

Explanation:-

The motion of the particle is arbitrary. The acceleration of the particle may also be non-uniform. Hence, this equation cannot represent the motion of the particle in space.

Explanation:-

The motion of the particle is arbitrary; acceleration of the particle may also be non-uniform. Hence, this equation cannot represent the motion of a particle in space.

Explanation:-

The arbitrary motion of the particle can be represented by this equation.

Answered by Pragya Singh | 1 year ago

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