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

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