The graph below represents the net force applied to a 1600 kg vehicle.
- Calculate the total impulse exerted on the vehicle over the 52 second interval. (2 marks)
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- If the vehicle begins at rest, determine its speed at the end of the 52 seconds. (2 marks)
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a. Total impulse is given by the area under the force-time graph:
The area under the graph can be split up as seen below:
\(\text{Area 1}\ =400 \times 12 = 4800\ \text{Ns}\).
\(\text{Area 2}\ = \dfrac{1}{2} \times 400 \times 8 = 1600\ \text{Ns}\)
\(\text{Area 3}\ = \dfrac{1}{2} \times 800 \times 8 = 3200\ \text{Ns}\)
\(\text{Area 4}\ = 800 \times 8 = 6400\ \text{Ns}\)
\(\text{Area 5}\ = \dfrac{1}{2} \times 800 \times 16 = 6400\ \text{Ns}\)
\(\therefore\) The total impulse exerted on the vehicle is \(22\,400\ \text{Ns}\).
| b. | \(I\) | \(=\Delta p\) |
| \(I\) | \(=mv-mu\) | |
| \(22\,400\) | \(=1600v-1600 \times 0\) | |
| \(v\) | \(=\dfrac{22\,400}{1600}\) | |
| \(=14\ \text{ms}^{-1}\) |
\(\therefore\) The final speed of the vehicle is \(14\ \text{ms}^{-1}\).
