Use forces to predict motion

Resolve forces along a chosen axis and use the signed resultant in F = ma. Acceleration can also be written v dv/dx when force depends on position rather than time.

Momentum is mass times velocity. Its change equals impulse, the time integral of resultant force. In straight-line motion, integrating acceleration yields velocity and integrating velocity yields position; both require initial conditions.

\displaystyle F=ma,\quad a=\frac{dv}{dt}=v\frac{dv}{dx},\quad\Delta p=\int F\,dt

WORKED EXAMPLE

A 2 kg body starts at 1 m/s under a constant resultant force of 6 N. Find its speed after 4 s.

Acceleration is $\frac{6}{2}$ = 3 m/s².
Velocity is 1 + 3t.
At 4 s, velocity is 13 m/s, positive in the chosen direction.

Assumed knowledge

Relate position, velocity and acceleration using differentiation and integration. Resolve vectors into components, use signed directions and consistent units, and apply initial conditions.

Study Specialist Mathematics alongside, or after, Mathematical Methods. Later units build on earlier units.

QCAA prior-learning guidance ↗

Use forces to predict motion

A 2 kg body starts at 1 m/s under a constant resultant force of 6 N. Find its speed after 4 s.

Put the idea to work.