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Chapter 2: Problem 231

A particle moves with a constant acceleration $\left(2 \mathrm{~m} / \mathrm{s}^{2}\right)\( Its initial velocity is \)10 \mathrm{~m} / \mathrm{s}$. Find velocity after \(\mathrm{t}\) second. (A) \((10+\mathrm{t}) \mathrm{ms}^{-1}\) (B) \(5(2+\mathrm{t}) \mathrm{ms}^{-1}\) (C) \(2(5+\mathrm{t}) \mathrm{ms}^{-1}\) (D) \(\left(10+\mathrm{t}^{2}\right) \mathrm{ms}^{-1}\)

Short Answer

Expert verified
The short answer is: \(v = (10 + t) \mathrm{ms}^{-1}\)

Step by step solution

01

Use the velocity formula

To find the velocity after t seconds, apply the formula for the velocity of a particle under constant acceleration: v = u + a*t
02

Plug in the given values

Plug in the given values of initial velocity and constant acceleration: v = 10 m/s + (2 m/s^2) * t
03

Simplify the expression

Simplify the expression by multiplying acceleration (2 m/s^2) with time (t): v = 10 m/s + 2t m/s The particle's velocity after t seconds will be: v = (10 + t) m/s So, the correct answer is: (A) \((10+\mathrm{t}) \mathrm{ms}^{-1}\)

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Most popular questions from this chapter

A particle goes from point \(\mathrm{A}\) to \(\mathrm{B}\). Its displacement is \(\mathrm{X}\) and path length is \(\mathrm{y}\). So $\mathrm{x} / \mathrm{y} \ldots$ \((\mathrm{A})>1\) (B) \(<1\) (C) \(\geq 1\) (D) \(\leq 1\)

\(x\) and y co-ordinates of a particle moving in \(\mathrm{x}-\mathrm{y}\) plane at some instant are \(\mathrm{x}=2 \mathrm{t}^{2}\) and $\mathrm{y}=(3 / 2) \mathrm{t}^{2}\( Calculate y co-ordinate when its \)\mathrm{x}\( coordinate is \)8 \mathrm{~m}$. (A) \(3 \mathrm{~m}\) (B) \(6 \mathrm{~m}\) (C) \(8 \mathrm{~m}\) (D) \(9 \mathrm{~m}\)

A car covers one third part of its straight path with speed \(\mathrm{V}_{1}\) and the rest with speed \(\mathrm{V}_{2}\). What is its average speed? (A) $\left[\left(3 \mathrm{v}_{1} \mathrm{v}_{2}\right) /\left(2 \mathrm{v}_{1}+\mathrm{v}_{2}\right)\right]$ (B) $\left[\left(2 \mathrm{v}_{1} \mathrm{v}_{2}\right) /\left(3 \mathrm{v}_{1}+\mathrm{v}_{2}\right)\right]$ (C) $\left[\left(3 \mathrm{v}_{1} \mathrm{v}_{2}\right) /\left(\mathrm{v}_{1}+2 \mathrm{v}_{2}\right)\right]$ (D) $\left[\left(3 \mathrm{v}_{1} \mathrm{v}_{2}\right) /\left(2 \mathrm{v}_{1}+2 \mathrm{v}_{2}\right)\right]$

\(\mathrm{P}^{\rightarrow}=\mathrm{Q}^{\rightarrow}\) is true, if \(\ldots\) (A) their magnitudes are equal (B) they are in same direction (C) their magnitudes are equal and they are in same direction (D) their magnitudes are not equal and they are not in same direction

Rohit completes a semicircular path of radius \(\mathrm{R}\) in 10 seconds. Calculate average speed and average velocity in \(\mathrm{ms}^{-1}\) (A) \([(2 \pi R) / 10],(2 R / 10)\) (B) \((\pi R / 10),(\mathrm{R} / 10)\) (C) \((\pi R / 10),(2 R / 10)\) (D) \([(2 \pi R) / 10],(\mathrm{R} / 10)\)
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