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Chapter 2: Problem 241

A particle moves in one direction with acceleration \(2 \mathrm{~ms}^{-2}\) and initial velocity \(3 \mathrm{~ms}^{-1}\).After what time its displacement will be \(10 \mathrm{~m}\) ? (A) \(1 \mathrm{~s}\) (B) \(2 \mathrm{~s}\) (C) \(3 \mathrm{~s}\) (D) \(4 \mathrm{~s}\)

Short Answer

Expert verified
(B) \(2 \mathrm{~s}\)

Step by step solution

01

Write down the given values

We have the following values given: Acceleration (a) = \(2 \mathrm{~ms}^{-2}\) Initial velocity (u) = \(3 \mathrm{~ms}^{-1}\) Displacement (s) = \(10 \mathrm{~m}\)
02

Use the equation \(s = ut + \frac{1}{2}at^2\) to solve for time (t)

Plugging in the given values, we get: \(10 = 3t + \frac{1}{2}(2)t^2\) Simplifying the equation: \(10 = 3t + t^2\)
03

Rearrange the equation to find t

Move the terms to one side: \(t^2 + 3t - 10 = 0\) Now, we need to solve this quadratic equation for t.
04

Solve the quadratic equation for t

We can solve this equation by factoring: \((t+5)(t-2) = 0\) Therefore, either t = -5 or t = 2. However, time cannot be negative, so we can dismiss the -5 as a solution. Thus, t = \(2 \mathrm{~s}\). Our answer is (B) \(2 \mathrm{~s}\).

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Most popular questions from this chapter

Velocity of particle \(\mathrm{A}\) with respect to particle \(\mathrm{B}\) is \(4(\mathrm{~m} / \mathrm{s})\) while they are moving in same direction. And it is \(10(\mathrm{~m} / \mathrm{s})\) while they are in opposite direction. What are the velocities of the particles with respect to the stationary frame of reference. (A) \(7 \mathrm{~ms}^{-1}, 3 \mathrm{~ms}^{-1}\) (B) \(4 \mathrm{~ms}^{-1}, 5 \mathrm{~ms}^{-1}\) (C) \(7 \mathrm{~ms}^{-1}, 4 \mathrm{~ms}^{-1}\) (D) \(10 \mathrm{~ms}^{-1}, 4 \mathrm{~ms}^{-1}\)

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$ \mathrm{A}^{\rightarrow}=3 \hat{\imath}+2 \hat{\jmath}-5 \mathrm{k}^{\wedge}\( and \)\mathrm{B}^{\rightarrow}=\hat{\imath}+\hat{\jmath}+2 \mathrm{k}^{\wedge}\( Find \)\left|\mathrm{A}^{\rightarrow}+2 \mathrm{~B}^{\rightarrow}\right|$ (A) \(\sqrt{40}\) (B) \(\sqrt{42}\) (C) \(\sqrt{39}\) (D) 2

\(x\) 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) \(9 \mathrm{~m}\)
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