📘 Physics Notes – Unit 1: Mechanics
1.1 Kinematics in 1D and 2D
Key Ideas:
• Position, displacement, velocity, acceleration are vector quantities.
• In 2D motion, break vectors into x and y components.
• Motion in each axis is independent (except for time being shared).
Equations of Motion (constant acceleration):
• 1D:
v=v0+atv=v0+atx=x0+v0t+12at2x=x0+v0t+21at2v2=v02+2a(x−x0)v2=v02+2a(x−x0)
• 2D: Projectile Motion (no air resistance)
x(t)=v0xtx(t)=v0xty(t)=v0yt−12gt2y(t)=v0yt−21gt2
Common Struggle Point: separating horizontal and vertical motion in projectiles.
Example:
A ball is launched at 20 m/s20m/s at 30∘30∘.
• v0x=20cos30=17.3 m/sv0x=20cos30=17.3m/s
• v0y=20sin30=10 m/sv0y=20sin30=10m/s
• Time of flight: t=2v0yg=209.8≈2.04 st=g2v0y=9.820≈2.04s
• Range: R=v0xt=17.3×2.04≈35.3 mR=v0xt=17.3×2.04≈35.3m
1.2 Newton’s Laws of Motion
• 1st Law: Inertia – an object remains at rest or constant velocity unless acted on by a net
force.
• 2nd Law:
F⃗net=ma⃗Fnet=ma
• 3rd Law: For every action, equal and opposite reaction.
1.1 Kinematics in 1D and 2D
Key Ideas:
• Position, displacement, velocity, acceleration are vector quantities.
• In 2D motion, break vectors into x and y components.
• Motion in each axis is independent (except for time being shared).
Equations of Motion (constant acceleration):
• 1D:
v=v0+atv=v0+atx=x0+v0t+12at2x=x0+v0t+21at2v2=v02+2a(x−x0)v2=v02+2a(x−x0)
• 2D: Projectile Motion (no air resistance)
x(t)=v0xtx(t)=v0xty(t)=v0yt−12gt2y(t)=v0yt−21gt2
Common Struggle Point: separating horizontal and vertical motion in projectiles.
Example:
A ball is launched at 20 m/s20m/s at 30∘30∘.
• v0x=20cos30=17.3 m/sv0x=20cos30=17.3m/s
• v0y=20sin30=10 m/sv0y=20sin30=10m/s
• Time of flight: t=2v0yg=209.8≈2.04 st=g2v0y=9.820≈2.04s
• Range: R=v0xt=17.3×2.04≈35.3 mR=v0xt=17.3×2.04≈35.3m
1.2 Newton’s Laws of Motion
• 1st Law: Inertia – an object remains at rest or constant velocity unless acted on by a net
force.
• 2nd Law:
F⃗net=ma⃗Fnet=ma
• 3rd Law: For every action, equal and opposite reaction.
