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Identify the final time value on the x-axis.

Mathematics

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4 parts
i

50 s\text{50 s}

ii

30 m/s\text{30 m/s}

iii

1.5 m/s2\text{1.5 m/s}^2

iv

1050 m\text{1050 m}

Step-by-step solution

8 steps

Here are the solutions based on the velocity-time graph:

Part i· 1 step

**The total time taken for the journey.

  1. Identify the final time value on the x-axis.

    The graph starts at t=0t=0 s and ends at t=50t=50 s.
    The total time taken is 50 s\boxed{\text{50 s}}.

Part ii

30 m/s\text{30 m/s}

**The maximum velocity reached.

  1. Identify the highest point on the y-axis (velocity axis) that the graph reaches.

    The highest velocity shown on the graph is 30 m/s.
    The maximum velocity reached is 30 m/s\boxed{\text{30 m/s}}.

Part iii

1.5 m/s2\text{1.5 m/s}^2

**The acceleration during the first 20 seconds.

  1. Recall that acceleration is the gradient of a velocity-time graph.

    The acceleration aa is given by the formula a=ΔvΔt=vf−vitf−tia = \frac{\Delta v}{\Delta t} = \frac{v_f - v_i}{t_f - t_i}.

  2. Identify the initial and final velocities and times for the first 20 seconds.

    Initial velocity (viv_i) at ti=0t_i = 0 s is 0 m/s.
    Final velocity (vfv_f) at tf=20t_f = 20 s is 30 m/s.

  3. Substitute the values into the formula and calculate.

    a=30 m/s−0 m/s20 s−0 s=30 m/s20 s=1.5 m/s2a = \frac{30 \text{ m/s} - 0 \text{ m/s}}{20 \text{ s} - 0 \text{ s}} = \frac{30 \text{ m/s}}{20 \text{ s}} = 1.5 \text{ m/s}^2

    The acceleration during the first 20 seconds is 1.5 m/s2\boxed{\text{1.5 m/s}^2}.

Part iv

1050 m\text{1050 m}

**The total distance travelled.

  1. Recall that the total distance travelled is the area under the velocity-time graph.

    The shape under the graph is a trapezoid. The area of a trapezoid is given by A=12(a+b)hA = \frac{1}{2} (a+b)h, where aa and bb are the lengths of the parallel sides and hh is the height.

  2. Identify the lengths of the parallel sides and the height from the graph.

    The parallel sides are the time intervals where the velocity is non-zero.
    Length of the top parallel side (constant velocity section): 40 s−20 s=20 s40 \text{ s} - 20 \text{ s} = 20 \text{ s}.
    Length of the bottom parallel side (total time): 50 s−0 s=50 s50 \text{ s} - 0 \text{ s} = 50 \text{ s}.
    The height of the trapezoid (maximum velocity) is 30 m/s.

  3. Substitute the values into the formula and calculate.

    Distance=12(20 s+50 s)×30 m/s\text{Distance} = \frac{1}{2} (20 \text{ s} + 50 \text{ s}) \times 30 \text{ m/s} Distance=12(70 s)×30 m/s\text{Distance} = \frac{1}{2} (70 \text{ s}) \times 30 \text{ m/s} Distance=35 s×30 m/s\text{Distance} = 35 \text{ s} \times 30 \text{ m/s} Distance=1050 m\text{Distance} = 1050 \text{ m}

    The total distance travelled is 1050 m\boxed{\text{1050 m}}.

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