You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

v-t Graph

The velocity-...

Question

The velocity-time graph of a particle in one-dimensional motion is shown in the figure. Which of the following formulae is correct for describing the motion of the particle over the time interval $t_{1}$ to $t_{2}$ ?

x (t_{2}) = x (t_{1}) + v (t_{1}) (t_{2} - t_{1}) + (\frac{1}{2}) a (t_{2} - t_{1})^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

v (t_{2}) = v (t_{1}) + a (t_{2} - t_{1})

No worries! We‘ve got your back. Try BYJU‘S free classes today!

v_{a v e r a g e} = \frac{(x (t_{2}) - x (t_{1}))}{(t_{2} - t_{1})}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

a_{a v e r a g e} = \frac{(v (t_{2}) + v (t_{1}))}{(t_{2} - t_{1})}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $v_{a v e r a g e} = \frac{(x (t_{2}) - x (t_{1}))}{(t_{2} - t_{1})}$
When velocity time graph of a particle in one dimensional motion
Time internal $t_{1}$ to $t_{2}$

$V_{a v g} = \frac{x (t_{2}) - x (t_{1})}{t_{2} - t_{1}}$

Suggest Corrections

Similar questions

Q. The velocity-time graph of a particle in one-dimensional motion is shown in Which of the following formulae are correct for describing the motion of the particle over the time-interval t (a) x(t₂ ) = x(t₁) + v (t1) (t₂ – t₁) +(½) a (t₂ – t₁)₂ (b) v(t₂ ) = v(t₁) + a (t₂ – t₁) (c) vaverage = (x(t₂) – x(t1))/(t₂ – t₁) (d) aaverage = (v(t₂) – v(t1))/(t₂ – t₁) (e) x(t₂ ) = x(t₁) + vaverage (t₂ – t₁) + (½) aaverage (t₂ – t₁)₂ (f) x(t₂) – x(t₁) = area under the v-t curve bounded by the t-axis and the dotted line shown.

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.

Q. 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}

t_{2}

)

Q. For any arbitrary motion in space, which of the following relations are true : (a) v _average = (1/2) (v (t₁) + v (t₂)) (b) v _average = [r(t₂) - r(t₁) ] /(t₂ – t₁) (c) v (t) = v (0) + a t (d) r (t) = r (0) + v (0) t + (1/2) a t₂ (e) a _average =[ v (t2) - v (t₁ )] /( t₂ – t₁) (The ‘average’ stands for average of the quantity over the time interval t₁to t2)

From above graph choose correct option for $t_{1}$ to $t_{2}$ where $t_{1}$ is the time at which velocity of particle = 0 $t_{2}$ is the time at which velocity of particle is negative.

Join BYJU'S Learning Program

The velocity-time graph of a particle in one-dimensional motion is shown in the figure. Which of the following formulae is correct for describing the motion of the particle over the time interval t1 to t2?

The correct option is C vaverage=(x(t2)−x(t1))(t2−t1)When velocity time graph of a particle in one dimensional motion Time internal t1 to t2Vavg=x(t2)−x(t1)t2−t1

The velocity-time graph of a particle in one-dimensional motion is shown in the figure. Which of the following formulae is correct for describing the motion of the particle over the time interval $t_{1}$ to $t_{2}$ ?

The correct option is C $v_{a v e r a g e} = \frac{(x (t_{2}) - x (t_{1}))}{(t_{2} - t_{1})}$
When velocity time graph of a particle in one dimensional motion
Time internal $t_{1}$ to $t_{2}$

$V_{a v g} = \frac{x (t_{2}) - x (t_{1})}{t_{2} - t_{1}}$