### Vector Geometry

Many ways problem

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## Problem

Each of the following situations, A-D, shows a system of forces acting on a particle of given mass and the initial velocity of the particle. Work out the single extra constant force that can be added to this system, so that the particle would be brought instantaneously to rest at the specified time.

Mass and forces Initial velocity Time when at rest
A $\quantity{4}{s}$

Describe how the particle behaves over time if this extra force is applied, assuming all the given forces acting on the particle remain unchanged. Compare this with how the particle would have behaved if the extra force had not been applied.

### Now try these

Mass and forces Initial velocity Time when at rest
B $\quantity{2}{s}$
C $\quantity{3}{s}$
D $\quantity{2}{s}$