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General SciencePhysics: Motion
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Two bodies P and Q are moving with uniform velocity. The slope of the distance-time graph of P is less than the slope of the distance-time graph of Q. Which statement is correct?

A

P is faster than Q

B

Q is faster than P

C

Both have the same speed

D

P is stationary

Correct Answer

ЁЯФм SC тАв Science Concept & PrincipleGeneral SciencePhysics: Motion
Option B

Q is faster than P

Quick Summary:

In a distance-time graph, the speed of an object is represented by the slope of the line. Since the slope of body Q is greater than the slope of body P, it follows that Q travels a greater distance in the same amount of time, making Q faster than P.

ЁЯФмSCScience SolutionConcept & Principle
ЁЯТб Explanation

In a distance-time graph, the speed of an object is represented by the slope of the line. Since the slope of body Q is greater than the slope of body P, it follows that Q travels a greater distance in the same amount of time, making Q faster than P.

ЁЯТб Everyday Analogy (Real-World Intuition)

Think of two cars on a road: if car Q covers more distance than car P during the same 10-minute interval, car Q must be moving at a higher speed than car P.

ЁЯза Memory Mnemonic / Shortcut Aid

Slope = Speed; Steep = Swift.

ЁЯФв Key Formulas

v=╬Фs╬Фtv = \frac{\Delta s}{\Delta t}v=╬Фt╬ФsтАЛ тАФ definition of speed as the ratio of change in distance to change in time

Slope=tanтБб(╬╕)\text{Slope} = \tan(\theta)Slope=tan(╬╕) тАФ relation between the slope of a line and the angle it makes with the horizontal axis

тЪЩя╕П Working Principle

The speed of an object in uniform motion is defined as the rate of change of distance, given by v=dsdtv = \frac{ds}{dt}v=dtdsтАЛ. Graphically, this corresponds to the slope (mmm) of the distance-time plot, where m=tanтБб(╬╕)m = \tan(\theta)m=tan(╬╕). A steeper line (greater angle with the time axis) indicates a higher value of tanтБб(╬╕)\tan(\theta)tan(╬╕), directly corresponding to a higher uniform velocity.

ЁЯУМ Key Points
  • тЦ╕

    Distance-time graphs for uniform motion are always straight lines.

  • тЦ╕

    A horizontal line (slope = 0) represents a body at rest.

  • тЦ╕

    A steeper slope indicates higher speed.

ЁЯЫая╕П Applications / Uses
  • тЦ╕

    Analyzing vehicle performance in physics labs

  • тЦ╕

    Interpreting motion profiles in robotics

ЁЯУД Additional Information
  • тЦ╕

    Uniform velocity implies that acceleration is zero.

  • тЦ╕

    Option A is incorrect because P has a lower slope, implying lower speed.

  • тЦ╕

    Option C is incorrect because different slopes imply different speeds.

  • тЦ╕

    Option D is incorrect because a slope exists, so the body must be moving.

ЁЯУК Diagram / Illustration
DISTANCE-TIME GRAPH ANALYSISTime (t)Distance (s)Q (Steeper)P (Less steep)1. Principle:Speed (v) = Slope of d-t graph2. Formula:Slope = tan(╬╕) = ╬Фs / ╬Фt3. Observation:Slope(Q) > Slope(P)4. Conclusion:Higher slope = Higher speedFinal Verdict: Option B) Q is faster than PThe steeper the slope of a distance-time graph, the greater the speed.
тЬЕ

B is correct тАФ Q is faster than P because a steeper slope on a distance-time graph signifies a greater rate of displacement per unit time.

Core Concepts Used
Click any tag to open in AI Tutor
Uniform Motion Speed-Time Relationship Graphical Analysis of Motion
ЁЯТб EXAM TIP

Always check the axes labels; if the graph were velocity-time, the slope would represent acceleration, not speed!

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