Question:
A particle is thrown vertically up with an initial velocity 9 m/s from the surface of Earth ($take\, g \,= \,10 \,m/s^2$).The time taken by the particle to reach a height of $4\, m$ from the surface second time (in seconds) is
A particle is thrown vertically up with an initial velocity 9 m/s from the surface of Earth ($take\, g \,= \,10 \,m/s^2$).The time taken by the particle to reach a height of $4\, m$ from the surface second time (in seconds) is
Updated On: Jun 14, 2022
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The Correct Option is D
Solution and Explanation
Time taken by the particle to reach a height h from the surface of Earth is obtained from $h=ut-\frac{1}{2}gt^{2}$
Here, u = 9 m/s, h = 4 m, g = 10 m/s
$\therefore\quad4=9t-\frac{1}{2}\times10\times t^{2}$
4 = 9t - 5t or 5t - 9t + 4 = 0
5t - 5t - 4t + 4 = 0
$\Rightarrow\quad$ 5t(t - 1) - 4(t - 1) = 0
$\therefore\quad$ t = 1 s or $ t=\frac{4}{5}$ s
Hence, the time taken by the particle to reach a height of 4 m from the surface second time is 1 s.
Here, u = 9 m/s, h = 4 m, g = 10 m/s
$\therefore\quad4=9t-\frac{1}{2}\times10\times t^{2}$
4 = 9t - 5t or 5t - 9t + 4 = 0
5t - 5t - 4t + 4 = 0
$\Rightarrow\quad$ 5t(t - 1) - 4(t - 1) = 0
$\therefore\quad$ t = 1 s or $ t=\frac{4}{5}$ s
Hence, the time taken by the particle to reach a height of 4 m from the surface second time is 1 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.