First slide

Newton's laws of motion

Question

A body of mass 2 kg has an initial velocity of 3 meters per second along OE and it is subjected to a force of 4 N in a direction perpendicular to OE. The magnitude of displacement of the body from O after 4 seconds will be

Moderate

A

12 m
B

20 m
C

8 m
D

48 m

Solution

Displacement of body in 4 s along OE
$s_{x} = v_{x} t = 3 \times 4 = 12 m$
Force along OF (perpendicular to OE)
$\begin{array}{l} = 4 N \\ ∴ a_{y} = \frac{F}{m} = \frac{4}{2} = 2 m / s^{2} \end{array}$
Displacement of body in 4 s along OF
$\begin{array}{l} \Rightarrow s_{y} = u_{y} t + \frac{1}{2} a_{y} t^{2} = \frac{1}{2} \times 2 \times (4)^{2} = 16 m [As u_{y} = 0] \\ ∴ Net displacement s = \sqrt{s_{x}^{2} + s_{y}^{2}} = \sqrt{(12)^{2} + (16)^{2}} = 20 m \end{array}$

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