Question:
A body covers a distance of $4\, m$ in $3^{rd}$ second and $12 \,m$ in $5^{th}$ second. If the motion is uniformly accelerated, how far will it travel in the next $3$ seconds ?
A body covers a distance of $4\, m$ in $3^{rd}$ second and $12 \,m$ in $5^{th}$ second. If the motion is uniformly accelerated, how far will it travel in the next $3$ seconds ?
Updated On: Jul 5, 2022
- $10\,m$
- $30\,m$
- $40\,m$
- $60\,m$
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The Correct Option is D
Solution and Explanation
$S_{3}=u+\frac{a}{2}\left(2\times3-1\right)=4$ or $u+\frac{5}{2} a=4$
$S_{5}=u+\frac{a}{2}\left(2\times5-1\right)=12$ or $u+\frac{9}{2}a=12$
On solving, $u=-6\,m\,s^{-1}, a=4\,m\,s^{-2}$
Distance travelled in next $3$ seconds $=S_{8}-S_{5}$
$=\left[-6\times8+\frac{1}{2}\times4\times\left(8\right)^{2}\right]-\left[-6\times5+\frac{1}{2}\times4\times\left(5\right)^{2}\right]$
$=80-20=60\,cm$
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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.