Distance and displacement

    OCR
    GCSE

    Distance is defined as a scalar quantity representing the total path length covered by an object during motion, regardless of direction. In contrast, displacement is a vector quantity measuring the straight-line distance and specific direction from the starting point to the finishing point. Candidates must distinguish between these quantities to analyze motion accurately, particularly when calculating speed versus velocity. Mastery involves resolving vectors in one dimension and, for higher tiers, utilizing trigonometry or scale drawings for two-dimensional motion.

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    Objectives
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    Exam Tips
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    Pitfalls
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    Key Terms
    5
    Mark Points

    What You Need to Demonstrate

    Key skills and knowledge for this topic

    • Award 1 mark for stating that distance is a scalar quantity consisting of magnitude only
    • Award 1 mark for defining displacement as a vector quantity requiring both magnitude and direction
    • Credit responses that calculate resultant displacement using Pythagoras' theorem for perpendicular vectors
    • Award 1 mark for specifying the direction of displacement as a three-figure bearing or angle relative to a fixed point
    • Credit the correct use of a scale factor when determining displacement via scale drawing

    Marking Points

    Key points examiners look for in your answers

    • Award 1 mark for stating that distance is a scalar quantity consisting of magnitude only
    • Award 1 mark for defining displacement as a vector quantity requiring both magnitude and direction
    • Credit responses that calculate resultant displacement using Pythagoras' theorem for perpendicular vectors
    • Award 1 mark for specifying the direction of displacement as a three-figure bearing or angle relative to a fixed point
    • Credit the correct use of a scale factor when determining displacement via scale drawing

    Examiner Tips

    Expert advice for maximising your marks

    • 💡Always underline the words 'distance' or 'displacement' in the question stem; if displacement is requested, your answer is incomplete without a direction
    • 💡When using scale drawings, state your scale clearly (e.g., 1 cm = 10 m) and use a sharp pencil to ensure precision within tolerance limits
    • 💡For circular motion, remember that after one complete revolution, distance equals the circumference ($2\pi r$) while displacement is zero
    • 💡Use a protractor for bearings and ensure they are written as three figures (e.g., 045°)

    Common Mistakes

    Pitfalls to avoid in your exam answers

    • Simply adding the magnitudes of two perpendicular vectors (e.g., 3m + 4m = 7m) instead of calculating the hypotenuse
    • Stating the magnitude of displacement correctly but omitting the direction component entirely
    • Confusing zero displacement with zero distance when an object returns to its starting position
    • Using incorrect trigonometric ratios (sine/cosine) when resolving displacement vectors

    Study Guide Available

    Comprehensive revision notes & examples

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    Key Terminology

    Essential terms to know

    Scalar vs. Vector quantities
    Path length vs. Straight-line separation
    Vector addition and resultant displacement
    Directional notation and bearings

    Likely Command Words

    How questions on this topic are typically asked

    Define
    Calculate
    Determine
    Describe
    Explain
    Draw

    Practical Links

    Related required practicals

    • •{"code":"P2.3","title":"Measuring Speed","relevance":"Differentiation between speed (distance/time) and velocity (displacement/time)"}

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