Question:
A particle moving in a straight line covers half the distance with speed of $3 ms^{-1}$. The other half of the distance is covered in two equal time intervals with speed of $4.5\, ms^{-1}$ and $7.5\, ms^{-1}$ respectively. The average speed of the particle during this motion is
A particle moving in a straight line covers half the distance with speed of $3 ms^{-1}$. The other half of the distance is covered in two equal time intervals with speed of $4.5\, ms^{-1}$ and $7.5\, ms^{-1}$ respectively. The average speed of the particle during this motion is
Updated On: Mar 4, 2024
- 5
- 5.5
- 5.8
- 4
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The Correct Option is D
Solution and Explanation
Average speed of the particle for other half of the distances.
$A_{v} =\frac{2 \times 4.5 \times 7.5}{4.5+7.5}$
$=\frac{67.5}{12}=5.62$
Again, the average speed of the particle
$A_{v} =\frac{2 \times 5.63 \times 3}{5.63+3} $
$=3.9 \,m / s =4 \,m / s$
$A_{v} =\frac{2 \times 4.5 \times 7.5}{4.5+7.5}$
$=\frac{67.5}{12}=5.62$
Again, the average speed of the particle
$A_{v} =\frac{2 \times 5.63 \times 3}{5.63+3} $
$=3.9 \,m / s =4 \,m / s$
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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.