Question:
A particle moving with a uniform acceleration travels $24\, m$ and $64\,m$ in the first two consecutive interval of $4s$ each. Its initial velocity will be
A particle moving with a uniform acceleration travels $24\, m$ and $64\,m$ in the first two consecutive interval of $4s$ each. Its initial velocity will be
Updated On: Jun 20, 2022
- 5 m/s
- 3 m/s
- 1 m/s
- 4 m/s
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The Correct Option is C
Solution and Explanation
From equation of motion, we have
$s=u t+\frac{1}{2} a t^{2}$
where $s$ is displacement, $u$ is initial velocity, a is acceleration and $c$ is time.
When $s=24 \,m, t=4 s$,
we have
$24=4 u+\frac{1}{2} a(4)^{2}$
$\Rightarrow 24=4 u+8 a$
$\Rightarrow 6=u+2 a \,\,\,...$(i)
When body travels a total distance of $24+64=88$ min $8 s$, we get
$88=8 u+\frac{1}{2} a(8)^{2}$
$\Rightarrow 88=8 u+32 a$
$\Rightarrow 11=u+4 a \,\,\,...$(ii)
Solving Eqs. (i) and (ii), we get
$u=1\, m / s$
$s=u t+\frac{1}{2} a t^{2}$
where $s$ is displacement, $u$ is initial velocity, a is acceleration and $c$ is time.
When $s=24 \,m, t=4 s$,
we have
$24=4 u+\frac{1}{2} a(4)^{2}$
$\Rightarrow 24=4 u+8 a$
$\Rightarrow 6=u+2 a \,\,\,...$(i)
When body travels a total distance of $24+64=88$ min $8 s$, we get
$88=8 u+\frac{1}{2} a(8)^{2}$
$\Rightarrow 88=8 u+32 a$
$\Rightarrow 11=u+4 a \,\,\,...$(ii)
Solving Eqs. (i) and (ii), we get
$u=1\, m / s$
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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.