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The speed-time graph shows how a car comes to rest in 7 seconds. The part of the graph labelled PO is a straight line. Calculate (a) the deceleration of the car between t = 2 and t = 4

Physics

ScanSolve AI Answer

Answer

2.5 m/s2\text{}2.5\, \text{m/s}^2\text{}

Step-by-step solution

4 steps

Here's how to calculate the deceleration:

  1. Identify the coordinates of the points on the graph at t=2t=2 seconds and t=4t=4 seconds.

    At t1=2t_1 = 2 s, the speed v1=8v_1 = 8 m/s.
    At t2=4t_2 = 4 s, the speed v2=3v_2 = 3 m/s.

  2. Calculate the acceleration using the formula for the gradient of a speed-time graph.

    Acceleration a=change in speedchange in timea = \frac{\text{change in speed}}{\text{change in time}}

    a=v2−v1t2−t1a = \frac{v_2 - v_1}{t_2 - t_1}
  3. Substitute the values into the formula and calculate the acceleration.

    a=3 m/s−8 m/s4 s−2 sa = \frac{3\, \text{m/s} - 8\, \text{m/s}}{4\, \text{s} - 2\, \text{s}} a=−5 m/s2 sa = \frac{-5\, \text{m/s}}{2\, \text{s}} a=−2.5 m/s2a = -2.5\, \text{m/s}^2
  4. State the deceleration.

    Deceleration is the positive value of the negative acceleration.
    The acceleration is −2.5 m/s2-2.5\, \text{m/s}^2, so the deceleration is 2.5 m/s22.5\, \text{m/s}^2.

    The deceleration of the car between t=2t=2 and t=4t=4 is 2.5 m/s2\boxed{\text{}2.5\, \text{m/s}^2\text{}}

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