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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 A Answers

Skills

    1. (a) \(t = 2\) and \(t = 6\). \(v\) changes sign at both, so it changes direction at both.
    2. (b) \(t = 3\): at rest only at this time. v does not change sign (it is never negative), so it does not change direction.
    3. (c) \(t = 3.14\) s. \(v\) changes from positive to negative, so it changes direction.
    1. (a) −6 m
    2. (b) 15.3 m
    1. (a) 5 m s⁻¹
    2. (b) −9.05 m s⁻¹
    3. (c) 9.05 m s⁻¹
    1. (a) \(v = 24\), \(a = −30\): slowing down.
    2. (b) \(v = −12\), \(a = −6\): speeding up.
    3. (c) \(v = −12\), \(a = 6\): slowing down.

In context

    1. (a) \(t = 3\) and \(t = 4\)
    2. (b) Displacement 28.3 m, distance 29 m
    3. (c) \(v = −0.32\), \(a = −1.2\): speeding up.
    1. (a) 4 m s⁻²
    2. (b) \(t = 9\) s
    3. (c) 40 m
    4. (d) 72 m
    1. (a) \(t = 2\) and \(t = 6\)
    2. (b) 16 m
    3. (c) 48 m
    4. (d) \(t = 6\)

Stretch

    1. (a) \(t = 0.425\) s
    2. (b) 8 m s⁻¹
    3. (c) 31.9 m
    1. (a) \(s = t^{3} − 10t^{2} + 12t\)
    2. (b) \(t = 1.39\) s
    3. (c) \(v = −10.1\) m s⁻¹: moving in the negative direction

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