Q1. A 1000 kg car accelerates from rest to 20 m/s in 10 s. Find the force applied.
u = 0, v = 20 m/s, t = 10 s, m = 1000 kg
a = (v − u)/t = (20 − 0)/10 = 2 m/s²
F = m·a = 1000 × 2 = 2000 N
Force and Laws of Motion — Class 9
Forces don't move things — they *change* how they move. Use the F = ma calculator and the numericals engine to make Newton's three laws second nature.
ForceA push or pull that can change the state of motion, speed, direction or shape of a body. SI unit: newton (N).
InertiaThe tendency of a body to resist any change in its state of rest or motion. More mass ⇒ more inertia (Newton's first law).
Momentum (p)The "quantity of motion": p = mass × velocity = m·v. A vector, SI unit kg·m/s.
Newton's 2nd lawThe rate of change of momentum is proportional to the applied force, giving F = m·a (force = mass × acceleration).
Newton's Second Law calculator Interactive
Enter mass and acceleration to get the force — or read off momentum.
Force, F = m·a—N
Momentum, p = m·v—kg·m/s
The same force gives a small acceleration to a heavy body and a big acceleration to a light one — that is a = F/m.
Numericals practice Interactive
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Solved numericals
Q2. A bullet of 20 g is fired from a 4 kg gun at 200 m/s. Find the recoil velocity of the gun.
Conservation of momentum: 0 = m₁v₁ + m₂v₂
0 = (0.02)(200) + (4)(V)
V = −4/4 = −1 m/s (gun recoils at 1 m/s)
Formula sheet
| Quantity | Formula | SI unit |
|---|---|---|
| Newton's second law | F = m a | newton (N) |
| Momentum | p = m v | kg·m/s |
| Force as rate of change of momentum | F = (mv − mu) / t | N |
| Impulse | J = F·t = Δp | N·s |
| Conservation of momentum | m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ | — |
Common mistakes & exam wins
- First law = inertia (no force ⇒ no change in motion). Second law = F = ma. Third law = equal & opposite reaction.
- Convert grams to kilograms (÷1000) before using F = ma or p = mv.
- Action and reaction act on different bodies, so they never cancel out.
- Momentum is always conserved in collisions and explosions when no external force acts.
Frequently asked questions
What are Newton's three laws of motion?
1) A body stays at rest or in uniform motion unless acted on by a force (inertia). 2) F = m·a. 3) Every action has an equal and opposite reaction.
What is the SI unit of force?
The newton (N). One newton is the force that gives a 1 kg mass an acceleration of 1 m/s².
What is the law of conservation of momentum?
In the absence of an external force, the total momentum of a system before and after an interaction (collision/explosion) stays the same.
Why do passengers lurch forward when a bus stops suddenly?
Because of inertia of motion — the body tends to keep moving forward even though the bus has stopped.