Question:
A body of mass $2\, kg$ has an initial velocity of $3 m / s$ along $OE$ and it is subjected to a force of $4\, N$ in a direction perpendicular to $O E$. The distance of body from $O$ after $4 s$ will be :
A body of mass $2\, kg$ has an initial velocity of $3 m / s$ along $OE$ and it is subjected to a force of $4\, N$ in a direction perpendicular to $O E$. The distance of body from $O$ after $4 s$ will be :
Updated On: Jan 18, 2023
- 12 m
- 20 m
- 8 m
- 48 m
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The Correct Option is B
Solution and Explanation
The acceleration of the body perpendicular to $OE$ is :
$\alpha=\frac{F}{m}=\frac{4}{2}=2 m / s ^{2}$
Displacement along $O E ,$
$s_{1}=v t=3 \times 4=12 m$
Displacement perpendicular to $O E$
$ s_{2}=\frac{1}{2} a t^{2}$
$=\frac{1}{2} \times 2 \times(4)^{2}=16\, m$
The resultant displacement
$s=\sqrt{s_{1}^{2}+s_{2}^{2}}$
$=\sqrt{144+256}$
$=\sqrt{400} $
$=20 \,m$
$\alpha=\frac{F}{m}=\frac{4}{2}=2 m / s ^{2}$
Displacement along $O E ,$
$s_{1}=v t=3 \times 4=12 m$
Displacement perpendicular to $O E$
$ s_{2}=\frac{1}{2} a t^{2}$
$=\frac{1}{2} \times 2 \times(4)^{2}=16\, m$
The resultant displacement
$s=\sqrt{s_{1}^{2}+s_{2}^{2}}$
$=\sqrt{144+256}$
$=\sqrt{400} $
$=20 \,m$
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Concepts Used:
Motion in a straight line
The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion.
Types of Linear Motion:
Linear motion is also known as the Rectilinear Motion which are of two types:
- Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
- Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.