Read each statement below carefully and state with reasons and examples, if it is true or false; A particle in one-dimensional motion
with zero speed at an instant may have non-zero acceleration at that instant
True. A particle with zero speed at an instant can have non-zero acceleration at that instant. For example, a ball thrown vertically upward has zero speed at the highest point, but acceleration due to gravity (g = 9.8 m/s²) still acts downward at that instant.
with zero speed may have non-zero velocity,
False. Speed is the magnitude of velocity. If speed is zero, the magnitude of velocity is zero, which means velocity itself must be zero. It is impossible to have non-zero velocity with zero speed.
with constant speed must have zero acceleration,
True. In one-dimensional motion, if speed is constant, velocity must also be constant (since direction can only be positive or negative). If velocity is constant, acceleration must be zero. For example, a particle moving with constant velocity of 5 m/s has constant speed and zero acceleration.
with positive value of acceleration must be speeding up.
False. A particle with positive acceleration need not be speeding up. If the particle is moving in the negative direction (negative velocity) and has positive acceleration, the acceleration opposes the motion, causing the particle to slow down. For example, a particle moving left with velocity -10 m/s and acceleration +2 m/s² is slowing down, not speeding up.
Explanation
This question tests understanding of the relationship between speed, velocity, and acceleration in one-dimensional motion. Key concepts: (1) Speed is the magnitude of velocity, so zero speed means zero velocity. (2) Acceleration can exist even when velocity is momentarily zero (like at the turning point of projectile motion). (3) The sign of acceleration alone doesn't determine if an object is speeding up - the relative signs of velocity and acceleration matter. When velocity and acceleration have the same sign, the object speeds up; when they have opposite signs, it slows down.