A particle moving in unidirectional motion travels half of the total distance with a constant speed of 15 m/s. Now first half of the journey time it travels at 10 m/s and second half of the remaining journey time it travels at 5 m/s. Average speed of the particle is
- 12 m/s
- 10 m/s
- 7 m/s
- 9 m/s
The Correct Option is B
Solution and Explanation
Given:
The formula for average velocity: \[ v_{\text{av}} = \frac{\text{Displacement}}{\text{Time}} \]
Step-by-Step Solution:
1. Expression for Velocity:
Let the velocity expression be: \[ v_{\text{av}} = \frac{15}{x} + \frac{2t}{2x} \]
2. Simplification:
Combining terms: \[ v_{\text{av}} = \frac{15}{x} + \frac{10 + 5}{2x} \] Further simplification gives: \[ v_{\text{av}} = 10 \, \text{m/s} \]
Final Answer:
The correct answer is (B): 10 m/s.
Top Questions on Kinematics
- A particle moves along the x-axis and has its displacement x varying with time t according to the equation \( x = c_0 (t^2 - 2) + c (t - 2)^2 \) where \( c_0 \) and \( c \) are constants of appropriate dimensions. Then, which of the following statements is correct?
- JEE Main - 2025
- Physics
- Kinematics
- The velocity is given as \( \mathbf{v} = 3\hat{i} + 3\hat{j} \). Find the acceleration \( \mathbf{a} \).
- KEAM - 2025
- Mathematics
- Kinematics
- Which of the following curves possibly represent one-dimensional motion of a particle?
- JEE Main - 2025
- Physics
- Kinematics
- The angle of projection of a particle is measured from the vertical axis as $ \phi $ and the maximum height reached by the particle is $ h_m $. Here $ h_m $ as function of $ \phi $ can be presented as
- JEE Main - 2025
- Physics
- Kinematics
The motion of an airplane is represented by the velocity-time graph as shown below. The distance covered by the airplane in the first 30.5 seconds is km.
- JEE Main - 2025
- Physics
- Kinematics
Questions Asked in JEE Main exam
The total number of structural isomers possible for the substituted benzene derivatives with the molecular formula $C_7H_{12}$ is __
- JEE Main - 2025
- Organic Chemistry
Four capacitors each of capacitance $16\,\mu F$ are connected as shown in the figure. The capacitance between points A and B is __ (in $\mu F$)
- JEE Main - 2025
- Electrostatics
Among, Sc, Mn, Co and Cu, identify the element with highest enthalpy of atomisation. The spin only magnetic moment value of that element in its +2 oxidation state is _______BM (in nearest integer).
- JEE Main - 2025
- d block elements
X g of nitrobenzene on nitration gave 4.2 g of m-dinitrobenzene. X =_____ g. (nearest integer) [Given : molar mass (in g mol\(^{-1}\)) C : 12, H : 1, O : 16, N : 14]
- JEE Main - 2025
- Stoichiometry and Stoichiometric Calculations
A perfect gas (0.1 mol) having \( \bar{C}_V = 1.50 \) R (independent of temperature) undergoes the above transformation from point 1 to point 4. If each step is reversible, the total work done (w) while going from point 1 to point 4 is ____ J (nearest integer) [Given : R = 0.082 L atm K\(^{-1}\)]
- JEE Main - 2025
- Thermodynamics
Concepts Used:
Kinematics
Kinematics is a branch of physics that deals with the study of motion, without considering the forces that cause the motion. It is concerned with the position, velocity, and acceleration of objects, as well as the time it takes for them to move from one point to another.
In kinematics, the motion of an object is represented using mathematical equations and graphs. The most common quantities used in kinematics are displacement, velocity, acceleration, and time.
Displacement refers to the change in position of an object, and it is represented by the symbol Δx. Velocity is the rate at which an object's position changes over time, and it is represented by the symbol v. Acceleration is the rate at which an object's velocity changes over time, and it is represented by the symbol a.
Also Read: Kinematics Formula
By analyzing the relationships between these quantities, kinematics can be used to predict the motion of objects in different situations. For example, kinematics can be used to calculate the maximum height reached by a projectile, the distance traveled by a car during a given time, or the time it takes for a rollercoaster to complete a loop.
Kinematics is used in many areas of physics, including mechanics, astrophysics, and robotics. It is also used in engineering, where it is used to design and optimize the motion of machines and vehicles.