Question

A particle moves along a straight line such that its position (x) at any time (t) is given by x=(t^2-t)m where t is in seconds . Total distance travelled by the particle in first second is:
(A) 3/4 m
(B) 1/4 m
(C) 1/2 m
(D) Zero


Please answer in detail

Answer 1

Given :

• x = (t² - t) m

To Find :

• What is the Distance travelled by particle in 1st second

Explanation :

The particle is moving along a straight line such that the position (x) at any time (t) is given by the equation x = (t² - t) m. In this type of questions we have to put the value of time in t which is time interval.

Calculation :

We have to find the distance travelled by the particle in first seconds. So, we have to put here t as 1 s.

$\implies \sf{x \: = \: t^2 \: - \: t} \\ \\ \implies \sf{x \: = \: 1^2 \: - \: 1} \\ \\ \implies \sf{x \: = \: 1 \: - \: 1} \\ \\ \implies \sf{x \: = \: 0}$

$\therefore$ Distance travelled by particle in 1st second is 0 m.

It means particle was at rest in 1st second

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$\Large {\: \: \: \: \: \: \: \: {\underline{\underline{\red{\mathfrak{Additional \: Information}}}}}}$

Distance

• It is the actual path travelled by body.
• It is a scalar quantity.
• Distance can never be negative or zero.
• It can be zero only when object is in the state of rest.

Displacement

• It is the shortest path travelled by body.
• It is a vector quantity
• Displacement can be zero as well as positive.

Answer 2

$\huge\sf{ \underline{ \underline{Question}}}$

• A particle moves along a straight line such that its position (x) at any time (t) is given by $\sf{x\:=\:(\ t^{2}-t)m}$ where t is in seconds Total distance travelled by the particle in first second is ?

$\huge\sf{ \underline{ \underline{Answer}}}$

• $\sf{Zero}$

$\huge\sf{ \underline{ \underline{Solution}}}$

$\sf{x\:=\:(\ t^{2}-t)}$

$\bf{Time\:is\:1\:second}$

$\mapsto\sf{x\:=\:\ (1)^{2}-1}$

${}$

$\mapsto\sf{x\:=\:1\:-\:1}$

${}$

$\mapsto\sf{x\:=\:0}$

${}$

$\sf{ \purple{ \underline{So\: option\:(d)\:is\: Correct}}}$

$\sf{ }$

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• It's distance in first second is 0m

• It states that the particle was in rest in first second

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