Solution:

Solution:

Impulse is given by the change in momentum:

$$J = \Delta p = m \Delta v$$

From the graph, we find velocity before and after $t = 2s$:

• Before $t = 2s$:

  $$v_{\text{initial}} = \frac{x_2 - x_1}{t_2 - t_1} = \frac{0 - 20}{2 - 0} = -10 \text{ m/s}$$

• After $t = 2s$:

  $$v_{\text{final}} = \frac{x_3 - x_2}{t_3 - t_2} = \frac{20 - 0}{4 - 2} = 10 \text{ m/s}$$

Now, impulse:

$$J=m(v_{\text{final}}-v_{\text{initial}})$$

$$J = m (v_{\text{final}} - v_{\text{initial}})$$ $$J = 2 \times (10 - (-10)) = 2 \times 20 = 40 \text{ Ns}$$

Final Answer:

$$\mathbf{40 \text{ Ns}}$$