(B) The correct option is $(B)$.$(i)$ From $t=0 \, s$ to $t=2 \, s$,the position $x=0$,so the velocity $v = \frac{dx}{dt} = 0$.$(ii)$ From $t=2 \, s$

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Velocity of the particle is opposite to acceleration between $t=2 \, s$ to $t=5 \, s$.

(B) The correct option is $(B)$.$(i)$ From $t=0 \, s$ to $t=2 \, s$,the position $x=0$,so the velocity $v = \frac{dx}{dt} = 0$.$(ii)$ From $t=2 \, s$ to $t=5 \, s$,the slope of the $x-t$ graph is positive (velocity $v > 0$),but the graph is concave downwards,which implies acceleration $a $(iii)$ From $t=5 \, s$ to $t=8 \, s$,the slope of the $x-t$ graph is negative (velocity $v < 0$),and the graph is concave downwards (acceleration $a < 0$). Since both $v$ and $a$ are negative,they are in the same direction.

Class 11 Physics Motion in a Straight Line Instantaneous Velocity and Speed and Velocity-time Graph

Medium

The position-time graph of a particle moving along a straight line is shown,which is in the form of a semicircle starting from $t=2 \, s$ to $t=8 \, s$. Select the correct statement.

A
Velocity of the particle between $t=0 \, s$ to $t=2 \, s$ is positive.
B
Velocity of the particle is opposite to acceleration between $t=2 \, s$ to $t=5 \, s$.
C
Velocity of the particle is opposite to acceleration between $t=5 \, s$ to $t=8 \, s$.
D
Acceleration of the particle is positive between $t=2 \, s$ to $t=5 \, s$ while it is negative between $t=5 \, s$ to $t=8 \, s$.

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Class 11 Questions

Class 11

Physics Questions

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Motion in a Straight Line

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Instantaneous Velocity and Speed and Velocity-time Graph

The position $x$ of a particle moving in one dimension under the influence of a constant force is given by $t = \sqrt{x} + 3$,where $x$ is in meters and $t$ is in seconds. Find the displacement of the particle in $m$ when its velocity becomes zero.

Difficult

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If a steel ball is dropped from a height onto a marble floor,what will the velocity-time graph look like?

Medium

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The displacement-time graph of two moving particles makes angles of $30^{\circ}$ and $45^{\circ}$ with the time axis ($X$-axis). The ratio of their velocities is

EasyKCET 2011

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Match Column-$I$ with Column-$II$ based on the distance-time $(d-t)$ graphs provided in the image.
$(1)$ Velocity decreases $(a)$ Linear graph (constant slope)
$(2)$ Velocity increases $(b)$ Concave up graph (increasing slope)
$(3)$ Velocity is constant $(c)$ Concave down graph (decreasing slope)

Easy

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The figure shows a speed-time graph of a particle in motion along a constant direction. Three equal intervals of time are shown. In which interval is the average acceleration greatest in magnitude? In which interval is the average speed greatest? Choosing the positive direction as the constant direction of motion,give the signs of $v$ and $a$ in the three intervals. What are the accelerations at the points $A, B, C$ and $D$?

Medium

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$(1)$ Velocity decreases	$(a)$ Linear graph (constant slope)
$(2)$ Velocity increases	$(b)$ Concave up graph (increasing slope)
$(3)$ Velocity is constant	$(c)$ Concave down graph (decreasing slope)

The position-time graph of a particle moving along a straight line is shown,which is in the form of a semicircle starting from $t=2 \, s$ to $t=8 \, s$. Select the correct statement.

Similar Questions

The position $x$ of a particle moving in one dimension under the influence of a constant force is given by $t = \sqrt{x} + 3$,where $x$ is in meters and $t$ is in seconds. Find the displacement of the particle in $m$ when its velocity becomes zero.

If a steel ball is dropped from a height onto a marble floor,what will the velocity-time graph look like?

The displacement-time graph of two moving particles makes angles of $30^{\circ}$ and $45^{\circ}$ with the time axis ($X$-axis). The ratio of their velocities is

Match Column-$I$ with Column-$II$ based on the distance-time $(d-t)$ graphs provided in the image. $(1)$ Velocity decreases$(a)$ Linear graph (constant slope)$(2)$ Velocity increases$(b)$ Concave up graph (increasing slope)$(3)$ Velocity is constant$(c)$ Concave down graph (decreasing slope)

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Match Column-$I$ with Column-$II$ based on the distance-time $(d-t)$ graphs provided in the image.
$(1)$ Velocity decreases $(a)$ Linear graph (constant slope)
$(2)$ Velocity increases $(b)$ Concave up graph (increasing slope)
$(3)$ Velocity is constant $(c)$ Concave down graph (decreasing slope)