Kinematics Analysis: Motion of a Car via Speed-Time and Acceleration-Time Graphs

Kinematics Analysis: Motion of a Car via Speed-Time and Acceleration-Time Graphs

Secondary 3
  1. A car accelerates uniformly from rest until it reaches a speed of \(30\) m/s in \(20\) s.
    Calculate the acceleration of the car.
  2. The car continues to accelerate but at a slower rate for a further \(30\) s until it reaches a speed of \(40\) m/s.
    Then the car begins to slow down with uniform retardation of \(2.5\) m/s\(^{2}\).
    1. Draw the speed-time graph for the first \(50\) seconds of the journey.
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    2. Calculate the distance it travels during the period from \(t=20\) to \(t=50\).
    3. Calculate how long it would take for the car to come to rest.
    4. On the diagram in the answer space below, sketch the acceleration-time graph of the car for the entire journey.
      Indicate clearly the values on the vertical and horizontal axes.
    After sub-items image

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Answer:(a) \(1.5\text{ m/s}^2\). (b)(ii) \(1050\) m. (iii) \(16\) s after braking starts, at \(t=66\) s overall. (iv) \(1.5,1/3,-2.5\text{ m/s}^2\) on the three successive intervals.

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