A body at rest (v = 0) has zero velocity, zero momentum, and zero kinetic energy. However, it may still have potential energy (gravitational or elastic) and can have acceleration if a net force acts on it at that instant.
A body at rest has v=0, p=0, KE=0.
A body at rest MAY have potential energy (gravitational, elastic).
A body at rest MAY have acceleration (if a net force acts on it).
Example: ball at highest point — v=0 but a=g downward.
Potential energy depends on position, not on velocity.
A body at rest (velocity = 0):
CAN have:
Potential energy — gravitational (mgh) or elastic (½kx²) Example: A book on a table has gravitational PE = mgh. Example: A compressed spring at rest has elastic PE.
Acceleration — if a net force acts on it Example: A ball thrown vertically up has v=0 at the highest point, but a = g = 9.8 m/s² (downward). Example: A body released from rest has a = F/m > 0 at the initial instant.
Internal energy (thermal energy) — molecules still vibrate.
CANNOT have:
Summary: • KE = 0 ✓ (zero) • Momentum = 0 ✓ (zero) • PE → may be non-zero ✓ • Acceleration → may be non-zero ✓
Gravitational potential energy: PE = mgh • m = mass, g = 9.8 m/s², h = height above reference level • A stationary stone at height h = 10 m has PE = m × 9.8 × 10 (non-zero even at rest)
Elastic potential energy: PE = ½kx² • k = spring constant, x = compression/extension • A compressed spring at rest stores elastic PE.
Electric potential energy: • A stationary charged particle in an electric field has electric PE.
Key concept: Potential energy depends on position and configuration, NOT on motion. Hence, a body at rest can have potential energy.
A body can be momentarily at rest yet have non-zero acceleration.
Examples:
Ball at highest point (vertical throw): At the top: v = 0, but a = −g = −9.8 m/s² (downward)
Pendulum at extreme position: v = 0, but restoring force causes acceleration toward mean position.
Body released from rest: At t = 0: v = 0, but a = F/m (starts accelerating immediately).
An object in SHM at extreme position: v = 0, a = maximum (a = −ω²x)
Key distinction: Rest means v = 0 at that instant. Acceleration is rate of change of velocity (a = dv/dt), not velocity itself. So a body can be at rest AND accelerating simultaneously.
Conclusion: A body at rest may have: potential energy and acceleration. A body at rest cannot have: velocity, momentum, or kinetic energy.
A body at rest may have: (1) Potential energy — depends on position, not velocity. (2) Acceleration — if a net force acts (e.g., ball at highest point). It cannot have velocity, momentum, or kinetic energy.
Yes. A ball at the highest point of a vertical throw has velocity = 0 but acceleration = g = 9.8 m/s² downward. Acceleration is rate of change of velocity, not velocity itself.
No. KE = ½mv². If v = 0, then KE = 0. A body at rest always has zero kinetic energy.
A book on a table: it is at rest (v=0) but has gravitational PE = mgh (non-zero if h > 0).
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