Answer:
[tex](-32\,000)\; {\rm kg\cdot m\cdot s^{-1}}[/tex].
Explanation:
The momentum [tex]p[/tex] of a moving object is the product of its mass and velocity:
[tex](\text{momentum}) = (\text{mass})\, (\text{velocity})[/tex].
Assume that the velocity of the object changed from an initial value of [tex]u[/tex] to a new value of [tex]v[/tex]. Momentum would have changed from [tex]m\, u[/tex] to [tex]m\, v[/tex]. To find the change in momentum, subtract the initial value from the new value:
[tex]\begin{aligned} \Delta p &= (\text{new value}) - (\text{initial value}) \\ &= m\, v - m\, u \\ &= m\, (v - u)\end{aligned}[/tex].
In other words, when the velocity of an object changes while mass stays the same, the change in momentum would be equal to the product of mass and the change in velocity.
Assume that the mass of the vehicle in this question stays the same at [tex]m = 1600\; {\rm kg}[/tex]. Velocity would have change from the initial value of [tex]u = 20\; {\rm m\cdot s^{-1}}[/tex] to the new value of [tex]v = 0\; {\rm m\cdot s^{-1}}[/tex]. To find the change in velocity, subtract the initial value from the new value:
[tex](v - u) = 0\; {\rm m\cdot s^{-1}} - 20\; {\rm m\cdot s^{-1}} = (-20)\; {\rm m\cdot s^{-1}}[/tex].
The change in the momentum of the vehicle would be:
[tex]\begin{aligned} \Delta p &= m\, (v - u) \\ &= (1\, 600\; {\rm kg})\, ((-20)\; {\rm m\cdot s^{-1}}) \\ &= (-32\, 000)\; {\rm kg\cdot m\cdot s^{-1}}\end{aligned}[/tex].
The change in momentum is negative, meaning that the momentum of the vehicle is less than the initial value.
