First slide

Newton's laws of motion

Question

A particle of mass 2kgmoves with an initial velocity of $(4 \hat{i} + 2 \hat{j}) {ms}^{- 1}$ on the x-y plane. A force $\vec{F} = (2 \hat{i} - 8 \hat{j}) N$ acts on the particle. The initial position of the particle is (2 m,3 m). Then for y=3 m,

Moderate

A

Possible value of x is only x = 2 m
B

Possible value of x is not only x=2 m, but there exists some other value of x also
C

Time taken is 2 s
D

All of the above

Solution

$\vec{u} = 4 \hat{i} + 2 \hat{j}, \vec{a} = \frac{\vec{F}}{m} = \hat{i} - 4 \hat{j}$
Let at any time, the coordinates be (x, y)
$\begin{array}{l} x - 2 = u_{x} t + \frac{1}{2} a_{x} t^{2} \\ \Rightarrow x - 2 = 4 t + \frac{1}{2} t^{2} and y - 3 = 2 t - \frac{1}{2} 4 t^{2} \\ \Rightarrow y - 3 = 2 t - 2 t^{2} \end{array}$
$When y = 3 m, t = 0, 1 s; when t = 0, x = 2 m$
$When t = 1 s, x = 6.5 m$

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