(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 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

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Chapter

Motion in Straight Line

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Uniformly Accelerated Motion

$A$ bullet is fired into a fixed target and loses one-third of its velocity after traveling $4 \ cm$. It penetrates a further $D \times 10^{-3} \ m$ before coming to rest. The value of $D$ is:

MediumJEE MAIN 2024

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An automobile,travelling at $40\, km/h$,can be stopped at a distance of $40\, m$ by applying brakes. If the same automobile is travelling at $80\, km/h$,the minimum stopping distance,in metres,is (assume no skidding)..........$m$

MediumJEE MAIN 2018

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$A$ particle travels $10\,m$ in the first $5\,s$ and $10\,m$ in the next $3\,s$. Assuming constant acceleration,what is the distance travelled in the next $2\,s$ (in $m$)?

Difficult

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The distance travelled by a particle is proportional to the square of time. Then,the particle travels with:

Easy

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$A$ body travels for $15\, s$ starting from rest with constant acceleration. If it travels distances ${S_1}$,${S_2}$,and ${S_3}$ in the first $5\, s$,the second $5\, s$,and the next $5\, s$ respectively,the relation between ${S_1}$,${S_2}$,and ${S_3}$ is:

Difficult

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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?

Similar Questions

$A$ bullet is fired into a fixed target and loses one-third of its velocity after traveling $4 \ cm$. It penetrates a further $D \times 10^{-3} \ m$ before coming to rest. The value of $D$ is:

An automobile,travelling at $40\, km/h$,can be stopped at a distance of $40\, m$ by applying brakes. If the same automobile is travelling at $80\, km/h$,the minimum stopping distance,in metres,is (assume no skidding)..........$m$

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$A$ body travels for $15\, s$ starting from rest with constant acceleration. If it travels distances ${S_1}$,${S_2}$,and ${S_3}$ in the first $5\, s$,the second $5\, s$,and the next $5\, s$ respectively,the relation between ${S_1}$,${S_2}$,and ${S_3}$ is:

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