Following are four differrent relations about displacement, veloc… - Vidyadip

MCQ

Following are four differrent relations about displacement, velocity and acceleration for the motion of a particle in general. Choose the incorrect one (s):

A
$\text{v}_\text{av}=\frac{1}2\big[\text{v}(\text{t}_1)+\text{v}(\text{t}_2)\big]$
B
$\text{v}_\text{av}=\frac{r(\text{t}_2)-\text{r}(\text{t}_1)}{\text{t}_2-\text{t}_1}$
C
$\text{r}=\frac{1}2(\text{v}(\text{t}_2)-\text{v}(\text{t}_1))(\text{t}_2-\text{t}_1)$
D
$\text{a}_\text{av}=\frac{\text{v}(\text{t}_2)-\text{v}(\text{t}_1)}{\text{t}_2-\text{t}_1}$

✓

Answer

$\text{v}_\text{av}=\frac{1}2\big[\text{v}(\text{t}_1)+\text{v}(\text{t}_2)\big]$

$\text{r}=\frac{1}2(\text{v}(\text{t}_2)-\text{v}(\text{t}_1))(\text{t}_2-\text{t}_1)$

Explanation:

When an object covers a displacement $\Delta\text{r}$ in time $\Delta\text{t},$ its average velocity is given by $\vec{\text{v}}_\text{avg}=\frac{\overrightarrow{\Delta\text{r}}}{\Delta\text{t}}=\frac{\text{r}_2-\text{r}_1}{\text{t}_2-\text{t}_1}$ where r₁ and r₂ are position vectors corresponding to time t₁ and t₂.

If the velocity of an object changes from v₁ to v₂ in time $\Delta\text{t},$ average acceleration is given by

$\text{a}_\text{av}=\frac{\Delta\text{v}}{\Delta\text{t}}=\frac{\text{v}_2-\text{v}_1}{\text{t}_2-\text{t}_1}$

But, when acceleration is non-uniform,

$\text{v}_\text{av}\neq\frac{\text{v}_1+\text{v}_2}{2}$

Option (c) is similar to the relation $\vec{\text{r}}=\frac{1}2\text{at}^2$ which is not correct if initial velocity is given.

So (b) and (d) are the correct relations for the uniform acceleration.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Motion in a Plane→Motion in a Plane — all question types→Physics STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

A body, thrown upwards with some velocity reaches the maximum height of $50 \,m$. Another body with double the mass thrown up with double the initial velocity will reach a maximum height of............$m$

If the temperature of the sun were to be increased from $T$ to $2T$ and its radius from $R$ to $2R$ , then the ratio of the radiant energy received on the earth to what it was previously will be

The Poisson's ratio of a material is $0.5$. If a force is applied to a wire of this material, there is a decrease in the cross-sectional area by $4 \%$. The percentage increase in the length is ........ $\%$

$A$ solid cone hangs from $a$ frictionless pivot at the origin $O$, as shown. If $\hat i$ , $\hat j$ and $\hat k$ are unit vectors, and $a, b$, and $c$ are positive constants, which of the following forces $F$ applied to the rim of the cone at a point $P$ results in a torque $\tau$ on the cone with a negative component $\tau_Z$

Dimensions of $\frac{1}{(\mu_0\in_0)}$ is:

$\frac{\text{L}}{\text{T}}$
$\frac{\text{T}}{\text{L}}$
$\frac{\text{L}^2}{\text{T}^2}$
$\frac{\text{T}^2}{\text{L}^2}$

A gas has $n$ degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be.

A spring of spring constant $ 5 \times 10^3$ $ N/m$ is stretched initially by $5\,cm$ from the unstretched position. Then the work required to stretch it further by another $5\,cm$ is .............. $\mathrm{N-m}$

The angular speed of earth around its own axis is ......... $rad / s$

The driver of a bus approaching a big wall notices that the frequency of his bus's horn changes from $420\, Hz$ to $490\, Hz ,$ when he hears it after it gets reflected from the wall. Find the speed of the bus (in $kmh^{-1}$) if speed of the sound is $330\, ms ^{-1}$.

In the reported figure, two bodies $A$ and $B$ of masses $200\, {g}$ and $800\, {g}$ are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be $.....\,{rad} / {s}$ when ${k}=20 \,{N} / {m} .$