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Kinematics

Motion in a straight line and plane, projectile motion

Key Concepts
  • Displacement is a vector; distance is a scalar
  • Uniform acceleration: equations of motion apply directly
  • Projectile motion: horizontal (constant velocity) + vertical (free fall)
  • Relative velocity: v_AB = v_A − v_B
  • For maximum range of projectile: θ = 45°
Important Formulae
First equation of motion v = u + at
Second equation of motion s = ut + ½at²
Third equation of motion v² = u² + 2as
Range of projectile R = u²sin2θ / g
Maximum height H = u²sin²θ / 2g
Time of flight T = 2u sinθ / g
Quick Tips
  • At maximum height of a projectile, vertical velocity = 0; horizontal velocity is unchanged.
  • For equal ranges: angles θ and (90° − θ) give the same range.
  • Area under velocity–time graph = displacement; slope = acceleration.
Sample Practice Questions

  1. A car moving at 36 km/h is brought to rest in 5 s. Retardation:

    • 1 m/s²
    • 2 m/s²
    • 3 m/s²
    • 4 m/s²
    Show answer

    Answer: 2 m/s²

  2. The time of flight of a projectile on a horizontal plane is 2 s. Maximum height reached (g = 10 m/s²):

    • 2.5 m
    • 5 m
    • 10 m
    • 20 m
    Show answer

    Answer: 5 m

  3. Maximum height of a projectile launched with speed u at angle θ is:

    • u²sin²θ/g
    • u²sin²θ/2g
    • u²sinθ/2g
    • u²sin2θ/g
    Show answer

    Answer: u²sin²θ/2g

  4. A ball is thrown horizontally from a tower of height 20 m with speed 10 m/s. Time of flight (g = 10 m/s²):

    • 1 s
    • 2 s
    • √2 s
    • 4 s
    Show answer

    Answer: 2 s

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Practice Questions

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