Math  /  Data & Statistics

QuestionA velocity-time graph for an object moving along the xx-axis is shown in Figure Q3 (b). (i) Plot a graph of the acceleration versus time. (ii) Determine the average acceleration of the object in the time intervals t=5.0 s\mathrm{t}=5.0 \mathrm{~s} to t=15.0 s\mathrm{t}=15.0 \mathrm{~s} and t=0\mathrm{t}=0 to t=20.0 s\mathrm{t}=20.0 \mathrm{~s}.
Fiaure Q3 (b)

Studdy Solution
Calculate the average acceleration for the interval t=0 t = 0 to t=20 t = 20 seconds:
- The change in velocity Δv=8(8)=16m/s\Delta v = 8 - (-8) = 16 \, \text{m/s}. - The change in time Δt=200=20s\Delta t = 20 - 0 = 20 \, \text{s}. - Average acceleration aavg=ΔvΔt=1620=0.8m/s2 a_{\text{avg}} = \frac{\Delta v}{\Delta t} = \frac{16}{20} = 0.8 \, \text{m/s}^2 .
The average accelerations are:
- From t=5 t = 5 to t=15 t = 15 seconds: 1.6m/s2 1.6 \, \text{m/s}^2 . - From t=0 t = 0 to t=20 t = 20 seconds: 0.8m/s2 0.8 \, \text{m/s}^2 .

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