JEE Mains · Physics · STD 11 - Motion in straight line
- JEE Mains 2026
- Easy
- MCQ
The velocity (\(v\)) versus time (\(t\)) plot of a particle is shown in the figure, for a time interval of \(40\text{ s}\). The total distance travelled by the particle and the average velocity during this period are, respectively _______.
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(100\text{ m}\) and zero
Step-by-step Solution
Detailed explanation
The total distance travelled by the particle is equal to the sum of the magnitudes of the areas under the velocity-time graph.
Area of the first triangle (from \(t = 0\) to \(t = 20\text{ s}\)) is:
\(A_1 = \dfrac{1}{2} \times 20 \times 5 = 50\text{ m}\)
Magnitude of the area of the second triangle (from \(t = 20\) to \(t = 40\text{ s}\)) is:
\(|A_2| = \left| \dfrac{1}{2} \times 20 \times (-5) \right| = 50\text{ m}\)
Total distance \(= A_1 + |A_2| = 50 + 50 = 100\text{ m}\)
The total displacement is the algebraic sum of the areas under the velocity-time graph.
Total displacement \(= A_1 + A_2 = 50 - 50 = 0\text{ m}\)
Average velocity is the ratio of total displacement to total time.
Average velocity \(= \dfrac{\text{Total displacement}}{\text{Total time}} = \dfrac{0}{40} = 0\)
Answer: \(100\text{ m}\) and zero
Area of the first triangle (from \(t = 0\) to \(t = 20\text{ s}\)) is:
\(A_1 = \dfrac{1}{2} \times 20 \times 5 = 50\text{ m}\)
Magnitude of the area of the second triangle (from \(t = 20\) to \(t = 40\text{ s}\)) is:
\(|A_2| = \left| \dfrac{1}{2} \times 20 \times (-5) \right| = 50\text{ m}\)
Total distance \(= A_1 + |A_2| = 50 + 50 = 100\text{ m}\)
The total displacement is the algebraic sum of the areas under the velocity-time graph.
Total displacement \(= A_1 + A_2 = 50 - 50 = 0\text{ m}\)
Average velocity is the ratio of total displacement to total time.
Average velocity \(= \dfrac{\text{Total displacement}}{\text{Total time}} = \dfrac{0}{40} = 0\)
Answer: \(100\text{ m}\) and zero
More questions from Physics
- The mean intensity of radiation on the surface of the Sun is about \(10^{8}\,W/m^2.\) The \(rms\) value of the corresponding magnetic field is closet toJEE Mains 2019 Medium
- Two separate wires \(A\) and \(B\) are stretched by \(2 \,mm\) and \(4\, mm\) respectively, when they are subjected to a force of \(2\, N\). Assume that both the wires are made up of same material and the radius of wire \(B\) is 4 times that of the radius of wire \(A\). The length of the wires \(A\) and \(B\) are in the ratio of \(a : b\). Then \(a / b\) can be expressed as \(1 / x\) where \(x\) isJEE Mains 2021 Hard
- A alternating current at any instant is given by \(i=\left[6+\sqrt{56} \sin \left(100 \pi t+\frac{\pi}{3}\right)\right] A\). The rms value of the current is _________ A.JEE Mains 2024 Hard
- A vector has magnitude same as that of \(\overrightarrow{\mathrm{A}}-=3 \hat{\mathrm{j}}+4 \hat{\mathrm{j}}\) and is parallel to \(\overrightarrow{\mathrm{B}}=4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}\). The \(\mathrm{x}\) and \(y\) components of this vector in first quadrant are \(\mathrm{x}\) and \(3\) respectively where \(x\)= _______.JEE Mains 2024 Hard
- Given below are two statements : Statements \(I\) : Astronomical unit \((Au)\). Parsec \((Pc)\) and Light year \((ly)\) are units for measuring astronomical distances. Statements \(II:\) \(Au < Parsec ( Pc ) < ly\) In the light of the above statements. choose the most appropriate answer from the options given below:JEE Mains 2023 Medium
- A cup of coffee cools from \(90^{\circ} \mathrm{C}\) to \(80^{\circ} \mathrm{C}\) in t minutes when the room temperature is \(20^{\circ} \mathrm{C}\). The time taken by the similar cup of coffee to cool from \(80^{\circ} \mathrm{C}\) to \(60^{\circ} \mathrm{C}\) at the same room temperature is :JEE Mains 2025 Medium
More PYQs from JEE Mains
- Match List\(-I\) with List\(-II.\)
Choose the most appropriate answer from the option given below :List\(-I\) List\(-II\) \((a)\) Torque \((i)\) \({MLT}^{-1}\) \((b)\) Impulse \((ii)\) \({MT}^{-2}\) \((c)\) Tension \((iii)\) \({ML}^{2} {T}^{-2}\) \((d)\) Surface Tension \((iv)\) \({MI} {T}^{-2}\) JEE Mains 2021 Medium - Unpolarized light of intensity \(I\) is incident on a system of two polarizers, \(A\) followed by \(B.\) The intensity of emergent light is \(I/2.\) If a third polarizer \(C\) is placed between \(A\) and \(B,\) the intensity of emergent light is reduced to \(I/3 .\) The angle between the polarizers \(A\) and \(C\) is \(\theta \) . ThenJEE Mains 2018 Medium
- A thin solid disk of 1 kg is rotating along its diameter axis at the speed of 1800 rpm. By applying an external torque of \(25 \pi \mathrm{Nm}\) for 40 s, the speed increases to 2100 rpm. The diameter of the disk is ________ m.JEE Mains 2025 Medium
- In the given figure, the charge stored in \(6 \ \mu \mathrm{F}\) capacitor, when points \(A\) and \(B\) are joined by a connecting wire is _______ \(\mu \mathrm{C}\).
JEE Mains 2024 Hard