First slide

Newton's laws of motion

Question

A particle of mass 2 kg moves with an initial velocity of $\vec{v} = 4 \hat{i} + 4 \hat{j} {ms}^{- 1}$ . A constant force of $\vec{F} = - 20 \hat{j} N$ is applied on the particle. Initially, the particle was at (0, 0). The x-coordinate of the particle when its y-coordinate again becomes zero is given by

Moderate

A

1.2 m
B

4.8 m
C

6.0 m
D

3.2 m

Solution

$\vec{a} = \frac{\vec{F}}{m} = - 10 \hat{j} {({ms}^{- 1})}^{2}$
Displacement in y-direction
$\begin{array}{l} y = u t + \frac{1}{2} a t^{2} \\ \Rightarrow 0 = 4 \times t \times - \frac{1}{2} \times 10 \times t^{2} \\ t = \frac{4}{5} s \Rightarrow x = 4 t = 4 \times \frac{4}{5} = 3.2 m \end{array}$

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