The position-time graphs for two students A and B returning from school to their homes are shown in the figure.
A. A lives closer to the school
B. B lives closer to the school
C. A takes lesser time to reach home
D. A travels faster than B
E. B travels faster than A
Choose the correct answer from the options given below :
A. A lives closer to the school
B. B lives closer to the school
C. A takes lesser time to reach home
D. A travels faster than B
E. B travels faster than A
Choose the correct answer from the options given below :
Show Hint
In position-time graphs, the slope represents speed, and the y-intercept at a given time represents distance.
(A), (C) and (E) only
(A) and (E) only
(B) and (E) only
(A), (C) and (D) only
The Correct Option is B
Solution and Explanation
Step 1: Identify the Slopes
The slope of A is given as:
\( \text{slope}_A = V_A \)
The slope of B is given as:
\( \text{slope}_B = V_B \)
Step 2: Compare the Slopes
Since:
\( \text{slope}_B > \text{slope}_A \)
It follows that:
\( V_B > V_A \)
Step 3: Relate Velocity to Time
As velocity (\( V \)) is inversely related to time (\( t \)) for a given distance:
\( t_B < t_A \)
Conclusion:
The final answer is: (A) and (E) only.
Top Questions on distance and displacement
- Displacement \( s \) of a particle at time \( t \) is expressed as \( s = 2t^3 - 9t \). Find the acceleration at the time when the velocity vanishes.
- AP EAMCET - 2024
- Mathematics
- distance and displacement
- 100 Vernier scale divisions match with 99 main scale divisions of a slide caliper. If the value of each main scale division is 1 mm, then the Vernier constant is:
- OJEE - 2024
- Physics
- distance and displacement
- The velocity of a particular mass \( m \) is \( \vec{v} = 5 \hat{i} + 4 \hat{j} + 6 \hat{k} \) when at \( \vec{r} = -2 \hat{i} + 4 \hat{j} + 6 \hat{k} \). The angular momentum of the particle about the origin is:
- OJEE - 2024
- Physics
- distance and displacement
- Two equal positive point charges are separated by a distance $2 a$ The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge $q_0$ becomes maximum is $\frac{a}{\sqrt{x}}$ The value of $x$ is ______
- JEE Main - 2023
- Physics
- distance and displacement
A person moved from A to B on a circular path as shown in figure If the distance travelled by him is 60 m, then the magnitude of displacement would be Given ( Cos 135° = -0.7)
- JEE Main - 2022
- Physics
- distance and displacement
Questions Asked in JEE Main exam
- The expression given below shows the variation of velocity \( v \) with time \( t \): \[ v = At^2 + \frac{Bt}{C + t}. \] The dimension of \( ABC \) is:
- JEE Main - 2025
- Thermodynamics terms
- The elemental composition of a compound is 54.2%C, 9.2%H, and 36.6%O. If the molar mass of the compound is 132 g/mol, the molecular formula of the compound is:
- JEE Main - 2025
- Thermodynamics
Let A be a 3 × 3 matrix such that \(\text{det}(A) = 5\). If \(\text{det}(3 \, \text{adj}(2A)) = 2^{\alpha \cdot 3^{\beta} \cdot 5^{\gamma}}\), then \( (\alpha + \beta + \gamma) \) is equal to:
- JEE Main - 2025
- Matrix Operations
- Let \( P_n = \alpha^n + \beta^n \), \( P_{10} = 123 \), \( P_9 = 76 \), \( P_8 = 47 \), and \( P_1 = 1 \). The quadratic equation whose roots are \( \frac{1}{\alpha} \) and \( \frac{1}{\beta} \) is:
- JEE Main - 2025
- Sequences and Series
- Number of functions \( f: \{1, 2, \dots, 100\} \to \{0, 1\} \), that assign 1 to exactly one of the positive integers less than or equal to 98, is equal to:
- JEE Main - 2025
- Vectors