To find the change in velocity, you need to subtract the initial velocity from the final velocity.
The initial velocity \( v_i \) is +30 m/s and the final velocity \( v_f \) is -40 m/s. The change in velocity \( \Delta v \) can be calculated as follows:
\[ \Delta v = v_f - v_i \]
Substituting in the values:
\[ \Delta v = -40 , \text{m/s} - (+30 , \text{m/s}) \] \[ \Delta v = -40 , \text{m/s} - 30 , \text{m/s} \] \[ \Delta v = -70 , \text{m/s} \]
The magnitude of the change in velocity is \( 70 , \text{m/s} \), but since we typically express changes in velocity as a positive quantity when referring to their absolute magnitude, it is correct to state:
The change in velocity is 70 m/s.
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