ICSE Class 9 Physics – Derived Units and
Their Derivations
1. Motion in One Dimension
Speed (v): Speed = Distance / Time ⇒ Unit = m / s ⇒ SI Unit: m/s
Velocity (v): Same as speed but with direction ⇒ Unit = m / s ⇒ SI Unit: m/s
Acceleration (a): a = Change in velocity / Time ⇒ (m/s) / s = m/s² ⇒ SI Unit: m/s²
Displacement (s): Displacement is measured in length ⇒ SI Unit: metre (m)
Equations of motion
1. 1. v = u + at ⇒ (m/s) = (m/s) + (m/s²)(s)
2. 2. s = ut + ½ at² ⇒ (m) = (m/s)(s) + ½(m/s²)(s²)
3. 3. v² = u² + 2as ⇒ (m²/s²) = (m²/s²) + 2(m/s²)(m)
2. Laws of Motion
Force (F): F = mass × acceleration ⇒ F = kg × m/s² ⇒ SI Unit: kg·m/s² = newton (N)
Momentum (p): p = mass × velocity ⇒ kg × m/s ⇒ SI Unit: kg·m/s
Impulse: Impulse = Force × time ⇒ N·s = (kg·m/s²)·s = kg·m/s ⇒ Same as
momentum
Weight (W): W = mg ⇒ Unit = kg × m/s² = N (newton)
3. Gravitation
Gravitational Force (F): F = G·(m₁·m₂)/r² ⇒ Units: N = (N·m²/kg²)(kg·kg)/(m²)
G (Gravitational Constant): Unit of G = N·m²/kg² ⇒ Derived from Newton's law of
gravitation
g (acceleration due to gravity): g = F/m ⇒ g = N/kg ⇒ (kg·m/s²)/kg = m/s²
Potential Energy (PE): PE = mgh ⇒ kg·m²/s² ⇒ SI Unit: joule (J)
Their Derivations
1. Motion in One Dimension
Speed (v): Speed = Distance / Time ⇒ Unit = m / s ⇒ SI Unit: m/s
Velocity (v): Same as speed but with direction ⇒ Unit = m / s ⇒ SI Unit: m/s
Acceleration (a): a = Change in velocity / Time ⇒ (m/s) / s = m/s² ⇒ SI Unit: m/s²
Displacement (s): Displacement is measured in length ⇒ SI Unit: metre (m)
Equations of motion
1. 1. v = u + at ⇒ (m/s) = (m/s) + (m/s²)(s)
2. 2. s = ut + ½ at² ⇒ (m) = (m/s)(s) + ½(m/s²)(s²)
3. 3. v² = u² + 2as ⇒ (m²/s²) = (m²/s²) + 2(m/s²)(m)
2. Laws of Motion
Force (F): F = mass × acceleration ⇒ F = kg × m/s² ⇒ SI Unit: kg·m/s² = newton (N)
Momentum (p): p = mass × velocity ⇒ kg × m/s ⇒ SI Unit: kg·m/s
Impulse: Impulse = Force × time ⇒ N·s = (kg·m/s²)·s = kg·m/s ⇒ Same as
momentum
Weight (W): W = mg ⇒ Unit = kg × m/s² = N (newton)
3. Gravitation
Gravitational Force (F): F = G·(m₁·m₂)/r² ⇒ Units: N = (N·m²/kg²)(kg·kg)/(m²)
G (Gravitational Constant): Unit of G = N·m²/kg² ⇒ Derived from Newton's law of
gravitation
g (acceleration due to gravity): g = F/m ⇒ g = N/kg ⇒ (kg·m/s²)/kg = m/s²
Potential Energy (PE): PE = mgh ⇒ kg·m²/s² ⇒ SI Unit: joule (J)
