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The motion of an athlete running along a circular path with constant speed is an example of accelerated motion because ___________.
The mass of the athlete is constant
The athlete's speed is increasing
A constant external force is applied
The direction of motion changes continuously
The direction of motion changes continuously
Velocity is a vector quantity, meaning it depends on both magnitude (speed) and direction. Since an athlete running on a circular path constantly changes their direction at every point, the velocity is changing, which by definition constitutes acceleration.
Velocity is a vector quantity, meaning it depends on both magnitude (speed) and direction. Since an athlete running on a circular path constantly changes their direction at every point, the velocity is changing, which by definition constitutes acceleration.
Think of steering a bicycle around a curve; even if you keep your pedaling speed constant, you feel the bike 'leaning' into the turn, which is the physical sensation of centripetal acceleration caused by your change in direction.
VAC: Velocity, Acceleration, Change (Direction/Magnitude).
acтАЛ=rv2тАЛ тАФ Centripetal acceleration formula where v is speed and r is radius.
v=dtdrтАЛ тАФ Velocity as the rate of change of position vector.
In uniform circular motion, even if the speed v remains constant, the direction of the velocity vector is always tangent to the circular path. According to Newton's first law, a change in velocity requires a net force, known as centripetal force, which acts towards the center of the circle. This force results in centripetal acceleration, directed towards the center of the circular path.
Uniform circular motion is an accelerated motion.
Velocity is defined by both magnitude (speed) and direction.
Centripetal acceleration is always perpendicular to the instantaneous velocity.
Planetary motion in circular orbits
Car turning on a curved track
The centripetal force is not a 'new' force but the requirement for any force (like friction or gravity) to provide the necessary radial acceleration.
Option B is incorrect because speed is constant in uniform circular motion.
Option C is partially true as a force exists, but Option D defines the kinematic reason for acceleration.
D is correct тАФ The motion is accelerated because the direction of the velocity vector changes continuously, even if the speed remains constant.
Always remember that in physics, acceleration occurs whenever there is a change in the velocity vector, not just when the speed (magnitude) changes!
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