(B) Given that the displacement $x$ is proportional to the square of time $t$,we have $x = k t^{2}$,where $k$ is a constant.The velocity $v$ is the fi

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(B) Given that the displacement $x$ is proportional to the square of time $t$,we have $x = k t^{2}$,where $k$ is a constant.The velocity $v$ is the first derivative of displacement with respect to time: $v = \frac{dx}{dt} = \frac{d}{dt}(k t^{2}) = 2kt$.The acceleration $a$ is the derivative of velocity with respect to time: $a = \frac{dv}{dt} = \frac{d}{dt}(2kt) = 2k$.Since $k$ is a constant,$2k$ is also a constant. Therefore,the object has a constant acceleration.

Class 11 Physics Motion in a Straight Line Uniformly Accelerated Motion

Medium

If the displacement of an object moving along a straight line is proportional to the square of the time elapsed,does the object have a constant velocity or a constant acceleration?

A
Constant velocity
B
Constant acceleration
C
Increasing acceleration
D
Decreasing acceleration

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Class 11 Questions

Class 11

Physics Questions

Chapter

Motion in a Straight Line

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Uniformly Accelerated Motion

$A$ $150 \,m$ long train is moving with a uniform velocity of $45 \,km/h$. The time taken by the train to cross a bridge of length $850 \,m$ is..........$sec$.

Medium

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If a particle moves according to the equation $v = at$,what distance will it cover in the first $4 \, s$ (in $a$)?

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The distance $x$ covered by a particle in one-dimensional motion varies with time $t$ as $x^{2}=at^{2}+2bt+c$. If the acceleration of the particle depends on $x$ as $x^{-n}$,where $n$ is an integer,the value of $n$ is

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The displacement of a particle is given by $y = a + bt + ct^2 - dt^4$. The initial velocity and acceleration are respectively

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The initial velocity of a body moving along a straight line is $7 \, m/s$. It has a uniform acceleration of $4 \, m/s^2$. The distance covered by the body in the $5^{th}$ second of its motion is .......... $m$.

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If the displacement of an object moving along a straight line is proportional to the square of the time elapsed,does the object have a constant velocity or a constant acceleration?

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$A$ $150 \,m$ long train is moving with a uniform velocity of $45 \,km/h$. The time taken by the train to cross a bridge of length $850 \,m$ is..........$sec$.

If a particle moves according to the equation $v = at$,what distance will it cover in the first $4 \, s$ (in $a$)?

The distance $x$ covered by a particle in one-dimensional motion varies with time $t$ as $x^{2}=at^{2}+2bt+c$. If the acceleration of the particle depends on $x$ as $x^{-n}$,where $n$ is an integer,the value of $n$ is

The displacement of a particle is given by $y = a + bt + ct^2 - dt^4$. The initial velocity and acceleration are respectively

The initial velocity of a body moving along a straight line is $7 \, m/s$. It has a uniform acceleration of $4 \, m/s^2$. The distance covered by the body in the $5^{th}$ second of its motion is .......... $m$.

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