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Which of the following physical quantities represents the rate of change of velocity?
Speed
Velocity
Acceleration
Distance
Acceleration
Acceleration is defined as the rate of change of velocity with respect to time. Mathematically, it is the derivative of velocity vector with respect to time (a=dtdvтАЛ), representing how quickly an object speeds up, slows down, or changes its direction of motion.
Acceleration is defined as the rate of change of velocity with respect to time. Mathematically, it is the derivative of velocity vector with respect to time (a=dtdvтАЛ), representing how quickly an object speeds up, slows down, or changes its direction of motion.
When you press the accelerator pedal in a car or bike, the speedometer reading increases rapidly тАФ this change in speed (and thus velocity) per second is your acceleration.
Remember 'V-A-T': Velocity over Time gives Acceleration (a=tvтАЛ).
a=dtdvтАЛ тАФ Instantaneous acceleration
aavgтАЛ=╬Фt╬ФvтАЛ=tvтИТuтАЛ тАФ Average acceleration
LTтИТ2 тАФ Dimensional formula of acceleration
When an object's velocity (which has both magnitude and direction) changes over a time interval ╬Фt, the average acceleration is given by aavgтАЛ=╬Фt╬ФvтАЛ. The SI unit of acceleration is meter per second squared (m/s2 or mтЛЕsтИТ2), and its dimensional formula is [LTтИТ2].
Acceleration measures how fast velocity changes over time.
Since velocity is a vector quantity, a change in direction alone (at constant speed) also produces acceleration (e.g., uniform circular motion).
Retardation or deceleration is negative acceleration, where velocity decreases with time.
The slope of a velocity-time graph represents acceleration.
Helps in predicting the future position and velocity of moving bodies in kinematics.
Essential in designing vehicles, safety features, and understanding dynamics.
Calculating stopping distance of high-speed trains and cars.
Spacecraft trajectory and rocket launch dynamics.
Free-fall motion under gravity (gтЙИ9.8┬аm/s2).
Speed is the rate of change of distance (scalar quantity).
Velocity is the rate of change of displacement (vector quantity).
Distance is the total path length covered by a body (scalar quantity).
C is correct тАФ Acceleration is the physical quantity defined as the rate of change of velocity with respect to time.
In competitive exams like RRB ALP, always distinguish between speed (rate of change of distance) and velocity (rate of change of displacement), as well as velocity and acceleration (rate of change of velocity).
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