(D) Given the displacement equation: $\sqrt{x} = t + 7$.Squaring both sides,we get: $x = (t + 7)^2 = t^2 + 14t + 49$.The velocity $v$ is the rate of c

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The particle moves with constant acceleration

(D) Given the displacement equation: $\sqrt{x} = t + 7$.Squaring both sides,we get: $x = (t + 7)^2 = t^2 + 14t + 49$.The velocity $v$ is the rate of change of displacement with respect to time: $v = \frac{dx}{dt} = \frac{d}{dt}(t^2 + 14t + 49) = 2t + 14$.The acceleration $a$ is the rate of change of velocity with respect to time: $a = \frac{dv}{dt} = \frac{d}{dt}(2t + 14) = 2 \, m/s^2$.Since the acceleration $a = 2 \, m/s^2$ is a constant value,the particle moves with constant acceleration.

Class 11 Physics Motion in Straight Line Uniformly Accelerated Motion

Medium

If the displacement of a particle varies with time as $\sqrt{x} = t + 7$,then

A
Velocity of the particle is inversely proportional to $t$
B
Velocity of the particle is proportional to $t^2$
C
Velocity of the particle is proportional to $\sqrt{t}$
D
The particle moves with constant acceleration

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Motion in Straight Line

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Uniformly Accelerated Motion

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DifficultAIEEE 2005

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The relation between the position $x$ and time $t$ of a particle moving in one dimension is given by $t = \sqrt{x} + 3$,where $x$ is in meters and $t$ is in seconds. When the velocity of the particle becomes zero,the displacement of the particle is ........ $m$.

Medium

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MediumAIPMT 2008

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The velocity of a bullet is reduced from $200\; m/s$ to $100\; m/s$ while travelling through a wooden block of thickness $10\; cm$. The retardation,assuming it to be uniform,will be ........... $\times 10^4\; m/s^2$.

Difficult

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If the displacement of a particle varies with time as $\sqrt{x} = t + 7$,then

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The relation between time $t$ and distance $x$ is given by $t = \alpha x^2 + \beta x$,where $\alpha$ and $\beta$ are constants. If $v$ is the velocity,then what is the retardation?

$A$ bullet fired into a fixed target loses half of its velocity after penetrating $3\,cm$. How much further will it penetrate before coming to rest,assuming that it faces constant resistance to motion? (in $cm$)

The relation between the position $x$ and time $t$ of a particle moving in one dimension is given by $t = \sqrt{x} + 3$,where $x$ is in meters and $t$ is in seconds. When the velocity of the particle becomes zero,the displacement of the particle is ........ $m$.

$A$ particle moves in a straight line with a constant acceleration. It changes its velocity from $10 \, m/s$ to $20 \, m/s$ while passing through a distance of $135 \, m$ in $t$ seconds. The value of $t$ is..........$s$.

The velocity of a bullet is reduced from $200\; m/s$ to $100\; m/s$ while travelling through a wooden block of thickness $10\; cm$. The retardation,assuming it to be uniform,will be ........... $\times 10^4\; m/s^2$.

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