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Force, mass, velocity and acceleration

Two equations link the quantities in a motion problem. Acceleration is the change in velocity divided by the time taken, a = (v − u) ÷ t, where u is the starting velocity and v is the final velocity. Newton's second law says F = m × a.

Putting them together gives force = mass × (v − u) ÷ t. This shows how the changes are inter-related. For a given mass, a larger force gives a larger acceleration, so the velocity changes by a larger amount in the same time. For a given force, a larger mass gives a smaller change in velocity.

A 1200 kg car speeds up from rest to 20 m/s in 10 s. Its acceleration is 20 ÷ 10 = 2 m/s2, so the resultant force is 1200 × 2 = 2400 N.

A force can also slow an object down. An 800 kg car slows from 25 m/s to rest in 5 s. The change in velocity is 25 m/s, so the deceleration is 25 ÷ 5 = 5 m/s2 and the braking force is 800 × 5 = 4000 N. A force opposite to the motion will slow the object.

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