Answer:
Explanation:
When the velocity of an object changes, it would experience an impulse. If the mass of the object stays the same, and that the object moves along a line, the value of the impulse [tex]J[/tex] would be:
[tex]J = m \cdot \Delta v[/tex], where
On the other hand, the change in the object's velocity can be found with the equation:
[tex]\Delta v = v_{\text{final}} - v_\text{initial}[/tex].
Note that if [tex]m[/tex] is in [tex]\rm kg[/tex] and [tex]\Delta v[/tex] is in [tex]\rm m \cdot s^{-1}[/tex], the unit of [tex]J[/tex] would be [tex]\rm N \cdot s[/tex].
[tex]v_\text{initial} = 0\; \rm m \cdot s^{-1}[/tex].
[tex]v_\text{final} = 7.5\; \rm m \cdot s^{-1}[/tex].
[tex]\Delta v = v_{\text{final}} - v_\text{initial} = 7.5\; \rm m \cdot s^{-1}[/tex].
[tex]J = m \cdot \Delta v = 50 \times 7.5 = 375\; \rm N \cdot s[/tex].
[tex]v_\text{initial} = 12.0\; \rm m \cdot s^{-1}[/tex].
[tex]v_\text{final} = 0\; \rm m \cdot s^{-1}[/tex].
[tex]\Delta v = v_{\text{final}} - v_\text{initial} = -12.0\; \rm m \cdot s^{-1}[/tex]
[tex]J = m \cdot \Delta v = 50 \times 12.0 = 600\; \rm N \cdot s[/tex].
[tex]v_\text{initial} = 2.2\; \rm m \cdot s^{-1}[/tex].
[tex]v_\text{final} = 6.3\; \rm m \cdot s^{-1}[/tex].
[tex]\Delta v = v_{\text{final}} - v_\text{initial} = 4.1\; \rm m \cdot s^{-1}[/tex].
[tex]J = m \cdot \Delta v = 50 \times 4.1 = 201\; \rm N \cdot s[/tex].
[tex]v_\text{initial} = 2.5\; \rm m \cdot s^{-1}[/tex].
[tex]v_\text{final} = -2.5\; \rm m \cdot s^{-1}[/tex].
Note that [tex]v_\text{final}[/tex] and [tex]v_\text{initial}[/tex] are of opposite signs. The reason is that the object's velocity has changed direction in this period.
[tex]\Delta v = v_{\text{final}} - v_\text{initial} = -5.0\; \rm m \cdot s^{-1}[/tex].
[tex]J = m \cdot \Delta v = 50 \times (-5.0) = -250\; \rm N \cdot s[/tex].
