Question

A point object starts from rest from the origin and moves with a uniform acceleration (in $\left.\mathrm{m} \mathrm{s}^{-2}\right)$ of $\alpha \hat{\mathrm{i}}+\beta \hat{\mathrm{j}}+\gamma \hat{\mathrm{k}}$. The distance of the object from the origin after 1 second is (a) $\frac{\sqrt{\alpha^{2}+\beta^{2}+\gamma^{2}}}{2}$ (b) $\frac{\sqrt{\alpha \beta+\beta \gamma+\gamma \alpha}}{2}$ (c) $(\alpha+\beta+\gamma)$ (d) $\quad(\alpha+\beta+\gamma)^{2}$

Name: Problem 89, Chapter 2: IIT JEE Super Course in Physics: Mechanics I
Uploaded: 2021-06-08T04:45:42-08:00
Duration: 1 min 51 s
Channel: Satpal Satpal
Description: A point object starts from rest from the origin and moves with a uniform acceleration (in .m s^-2) of αî+βĵ+γk̂. The distance of the object from the origin after 1 second is (a) (√(α^2+β^2+γ^2))/(2) (b) (√(αβ+βγ+γα))/(2) (c) (α+β+γ) (d) (α+β+γ)^2

   A point object starts from rest from the origin and moves with a uniform acceleration (in $\left.\mathrm{m} \mathrm{s}^{-2}\right)$ of $\alpha \hat{\mathrm{i}}+\beta \hat{\mathrm{j}}+\gamma \hat{\mathrm{k}}$. The distance of the object from the origin after 1 second is
(a) $\frac{\sqrt{\alpha^{2}+\beta^{2}+\gamma^{2}}}{2}$
(b) $\frac{\sqrt{\alpha \beta+\beta \gamma+\gamma \alpha}}{2}$
(c) $(\alpha+\beta+\gamma)$
(d) $\quad(\alpha+\beta+\gamma)^{2}$

IIT JEE Super Course in Physics: Mechanics I

Trishna Knowledge… 1st Edition

Chapter 2, Problem 89

Instant Answer

Solved by Expert Satpal Satpal

06/08/2021

Step 1

We can find the magnitude of the acceleration as follows: \[|\vec{a}| = \sqrt{\alpha^{2}+\beta^{2}+\gamma^{2}}\] Show more…

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A point object starts from rest from the origin and moves with a uniform acceleration (in $\left.\mathrm{m} \mathrm{s}^{-2}\right)$ of $\alpha \hat{\mathrm{i}}+\beta \hat{\mathrm{j}}+\gamma \hat{\mathrm{k}}$. The distance of the object from the origin after 1 second is (a) $\frac{\sqrt{\alpha^{2}+\beta^{2}+\gamma^{2}}}{2}$ (b) $\frac{\sqrt{\alpha \beta+\beta \gamma+\gamma \alpha}}{2}$ (c) $(\alpha+\beta+\gamma)$ (d) $\quad(\alpha+\beta+\gamma)^{2}$

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Key Concepts

Displacement Under Uniform Acceleration

This concept involves determining the displacement of an object that starts from rest, where the displacement vector can be computed using the equation s = (1/2)*a*t². The equation shows that under constant acceleration, the distance traveled increases quadratically with time.

Uniform Acceleration

This concept refers to motion in which the acceleration remains constant in both magnitude and direction. It is fundamental for predicting motion over time, as it allows the use of simple kinematic equations to calculate displacement and velocity.

Vector Magnitude Calculation

In problems involving multi-dimensional motion, displacement is often described as a vector with components in different directions. Calculating the distance from a reference point, such as the origin, involves computing the magnitude of the displacement vector by taking the square root of the sum of the squares of its individual components.

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