For any arbitrary motion in space, which of the following relations are true:
(a) $v_{a v e r a g e} = (1 / 2) (v (t_{1}) + v (t_{2}))$
(b) $v_{a v e r a g e} = [r (t_{2}) - r (t_{1})] / (t_{2} - t_{1})$
(c) $v (t) = v (0) + a t$
(d) $r (t) = r (0) + v (0) t + (1 / 2) a$ $t^{2}$
(e) $a_{a v e r a g e} = [v (t_{2}) - v (t_{1})] / (t_{2} - t_{1})$
(The 'average' stands for average of the quantity over the time interval $t_{1}$ to $t_{2}$ )

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Solution

(a) Invalid for non uniform acceleration
(b) This is the mathematical definition of average velocity.

(c) This is valid only for constant acceleration
(d) Valid only for constant accelerations

(e) Mathematical definition of average acceleration
(b) and (e) are valid.

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Similar questions

The velocity-time graph of a particle in one-dimensional motion is shown in Fig. 3.29:

Which of the following formulae are correct for describing the motion of the particle over the time-interval t₂ to t₁?

(a) x(t₂) = x(t₁) + v(t₁)(t₂–t₁) + ()a(t₂–t₁)²

(b) v(t₂)= v(t₁) + a(t₂–t₁)

(d) a_Average = (v(t₂) – v(t₁)) / (t₂ – t₁)

(e) x(t₂) = x(t₁) + v_Average(t₂ – t₁) + ()a_Average(t₂ – t₁)²

(f) x(t₂) – x(t₁) = area under the v–t curve bounded by the t-axis and the dotted line shown.

For any arbitrary motion in space, which of the following relations are true:

(a)

(b)

(c)

(d)

(e)

(The ‘average’ stands for average of the quantity over the time interval t₁ to t₂)

t_{1}

t_{2}

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