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IB Mathematics: Applications and Interpretation HL · AHL 4: Vectors · AHL 4.22

Motion on a line: direction changes, distance and speed Problem set B Answers

Skills

    1. (a) \(t = 3\) and \(t = 7\). \(v\) changes sign at both, so it changes direction at both.
    2. (b) \(t = 5\): at rest only at this time. v does not change sign (it is never negative), so it does not change direction.
    3. (c) \(t = 0.785\) s. \(v\) changes from positive to negative, so it changes direction.
    1. (a) −5.33 m
    2. (b) 36.3 m
    1. (a) 7 m s⁻¹
    2. (b) −17 m s⁻¹
    3. (c) 17 m s⁻¹
    1. (a) \(v = 15\), \(a = −18\): slowing down.
    2. (b) \(v = −9\), \(a = −6\): speeding up.
    3. (c) \(v = −9\), \(a = 6\): slowing down.

In context

    1. (a) \(t = 2\) and \(t = 5\)
    2. (b) Displacement 18 m, distance 45 m
    3. (c) \(v = −3.75\), \(a = 6\): slowing down.
    1. (a) 3 m s⁻²
    2. (b) \(t = 11\) s
    3. (c) 84 m
    4. (d) 96 m
    1. (a) \(t = 3\) and \(t = 9\)
    2. (b) 36 m
    3. (c) 108 m
    4. (d) \(t = 9\)

Stretch

    1. (a) \(t = 0.680\) s
    2. (b) 12 m s⁻¹
    3. (c) 55.4 m
    1. (a) \(s = t^{3} − 13t^{2} + 16t\)
    2. (b) \(t = 1.38\) s
    3. (c) \(v = −14.1\) m s⁻¹: moving in the negative direction

jmaths.xyz · AI HL · AHL 4.22 Motion on a line: direction changes, distance and speed