Position (x) of a particle moving along x -axis varies with time (t) as shown in figure. average acc

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2.Motion in Straight Line

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The position $(x)$ of a particle moving along $x$-axis varies with time $(t)$ as shown in figure. The average acceleration of particle in time interval $t=0$ to $t=8 s$ is ........... $m / s ^2$

A$-5$

B$3$

C$-4$

D$2.5$

Solution

(b)
$t=0 \text { to } t=2 \quad \quad t=6 \text { to } t=8$
$v=20 \,m / s \quad \quad \quad v=-20 \,m / s$
$a_{\text {avg }}=\frac{\Delta v}{\Delta t}=\frac{-20-20}{8}=\frac{-40}{8}=-5\,ms ^{-2}$
$a_{\text {avg }}=-5 \,ms ^{-2}$

Standard 11

Physics

A particle of unit mass undergoes one dimensional motion such that its velocity varies according to $ v(x)= \beta {x^{ – 2n}}$, where $\beta$ and $n$ are constants and $x$ is the position of the particle. The acceleration of the particle as a function of $x$, is given by

hard

(AIPMT-2015)

The relation between time and distance is $t = \alpha {x^2} + \beta x$, where $\alpha $ and $\beta $ are constants. The retardation is

hard

(AIEEE-2005)

Velocity of a particle is in negative direction with constant acceleration in positive direction. Then, match the following columns.

Colum $I$ Colum $II$

$(A)$ Velocity-time graph $(p)$ Slope $\rightarrow$ negative

$(B)$ Acceleration-time graph $(q)$ Slope $\rightarrow$ positive

$(C)$ Displacement-time graph $(r)$ Slope $\rightarrow$ zero

$(s)$ $\mid$ Slope $\mid \rightarrow$ increasing

$(t)$ $\mid$ Slope $\mid$ $\rightarrow$ decreasing

$(u)$ |Slope| $\rightarrow$ constant

medium

Draw $x \to t$ graph for positive acceleration.

easy

Each of the three graphs represents acceleration versus time for an object that already has a positive velocity at time $t_1$. Which graphs show an object whose speed is increasing for the entire time interval between $t_1$ and $t_2$ ?

medium

Colum $I$	Colum $II$
$(A)$ Velocity-time graph	$(p)$ Slope $\rightarrow$ negative
$(B)$ Acceleration-time graph	$(q)$ Slope $\rightarrow$ positive
$(C)$ Displacement-time graph	$(r)$ Slope $\rightarrow$ zero
	$(s)$ $\mid$ Slope $\mid \rightarrow$ increasing
	$(t)$ $\mid$ Slope $\mid$ $\rightarrow$ decreasing
	$(u)$ \|Slope\| $\rightarrow$ constant

The position $(x)$ of a particle moving along $x$-axis varies with time $(t)$ as shown in figure. The average acceleration of particle in time interval $t=0$ to $t=8 s$ is ........... $m / s ^2$

Solution

Similar Questions

A particle of unit mass undergoes one­ dimensional motion such that its velocity varies according to $ v(x)= \beta {x^{ – 2n}}$, where $\beta$ and $n$ are constants and $x$ is the position of the particle. The acceleration of the particle as a function of $x$, is given by

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A particle of unit mass undergoes one dimensional motion such that its velocity varies according to $ v(x)= \beta {x^{ – 2n}}$, where $\beta$ and $n$ are constants and $x$ is the position of the particle. The acceleration of the particle as a function of $x$, is given by