A particle has an initial velocity of ( 3hat{i} + 4hat{j})ms^{-1} and an acceleration of (0.4hat{i}

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3-2.Motion in Plane

medium

A particle has an initial velocity of ($3\hat i + 4\hat j)\;ms^{-1}$ and an acceleration of $(0.4\hat i + 0.3\hat j)\;ms^{-2}$ Its speed after $10\;s$ is:

A$7 $ unit

B$8.5$ unit

C$10$ unit

D$7\sqrt 2 $ unit

(AIEEE-2009) (AIPMT-2010)

Solution

$\begin{array}{l}
Given\,\vec u = 3\hat i + 4\hat j,\hat a = 0.4\hat i + 0.3\hat j,t = 10s\\
\vec v = \vec u + \vec at = 3\hat i + 4\hat j + \left( {0.4\hat i + 0.3\hat j} \right) \times 10\\
= 7\hat i + 7\hat j\\
\therefore \left| {\vec v} \right| = \sqrt {{7^2} + {7^2}} = 7\sqrt 2 \,units
\end{array}$

Standard 11

Physics

$Y $ component of velocity is $20$ and $X$ component of velocity is $10$. The direction of motion of the body with the horizontal at this instant is

medium

A particle $(A)$ is dropped from a height and another particle $(B)$ is thrown in horizontal direction with speed of $5\; m/sec$ from the same height. The correct statement is

easy

(AIPMT-2002)

A mosquito is moving with a velocity $\overrightarrow{ v }=0.5 t ^{2} \hat{ i }+3 t \hat{ j }+9 \hat{ k }\, m / s$ and accelerating in uniform conditions. What will be the direction of mosquito after $2 \,s$ ?

hard

(JEE MAIN-2021)

The position of a particle is given by

$r=3.0 t \hat{i}+2.0 t^{2} \hat{j}+5.0 \hat{k}$

where $t$ is in seconds and the coefficients have the proper units for $r$ to be in metres.

$(a)$ Find $v (t)$ and $a (t)$ of the particle.

$(b)$ Find the magnitude and direction of $v (t)$ at $t=1.0 s$

medium

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medium

A particle has an initial velocity of ($3\hat i + 4\hat j)\;ms^{-1}$ and an acceleration of $(0.4\hat i + 0.3\hat j)\;ms^{-2}$ Its speed after $10\;s$ is:

Solution

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The position of a particle is given by

$r=3.0 t \hat{i}+2.0 t^{2} \hat{j}+5.0 \hat{k}$

where $t$ is in seconds and the coefficients have the proper units for $r$ to be in metres.

$(a)$ Find $v (t)$ and $a (t)$ of the particle.

$(b)$ Find the magnitude and direction of $v (t)$ at $t=1.0 s$