Motion and Kinematics Key Concepts
Posted on Oct 26, 2024 in Physics
Displacement and Distance
- The variation of the position vector that a particle experiences in a time interval is called displacement.
- The displacement vector is independent of the path followed by the particle.
- The distance traveled by a particle is greater than or equal to the magnitude of the displacement.
- The distance traveled is equal to the magnitude of displacement if the path is straight with no change in direction.
Velocity and Speed
- If a particle starts at point P and returns to P after a time Δt, the average velocity (vm) is zero.
- The instantaneous velocity vector is tangent to the path.
- The instantaneous speed is equal to the magnitude of the velocity vector.
- If a particle moves with constant velocity (v), its acceleration is 0.
Acceleration
- If a particle changes the magnitude of its velocity, tangential acceleration is generated. If it only changes direction, centripetal acceleration is generated.
- Curvilinear motion is always accelerated due to centripetal acceleration, as velocity changes direction.
Free Fall and Vertical Motion
- When an object falls freely from rest, the acceleration at the end of the sixth second is -9.8 m/s2.
- When an object is thrown vertically upwards, the speed decreases by 9.8 m/s2 every second while ascending.
Linear Motion
- In uniform linear motion, speed is constant and acceleration is zero.
- If a particle moves along a straight path, the normal acceleration is zero since velocity doesn’t change direction.
- For a particle moving on a straight line:
- In the position vs. time graph, the tangent represents instantaneous speed.
- In the velocity vs. time graph, the tangent represents acceleration, and the area under the curve represents displacement (algebraic sum) or distance (sum of absolute values).
- If the velocity vs. time graph changes sign, the particle changes its direction of motion.
- If speed changes by equal values in equal time intervals, the motion is uniformly accelerated.
Parabolic Motion
- Parabolic motion is curvilinear with constant acceleration.
- In parabolic motion, the horizontal velocity component is constant. At maximum height, the vertical velocity is zero.
- When launching a projectile, speed and gravity form a right angle at maximum height and an acute angle while descending.
- Projectile motion is composed of uniform rectilinear motion along the x-axis and uniformly accelerated rectilinear motion along the y-axis, with total acceleration equal to gravity.
- In projectile motion, the speed is the same at the same height, ascending or descending.
- Maximum range is achieved at a launch angle of 45°.
- Complementary launch angles result in equal ranges.
Circular Motion
- If a particle travels equal arcs in equal times, the motion is uniform circular.
- In uniform circular motion, velocity is tangent to the trajectory and perpendicular to total acceleration, which is equal to centripetal acceleration.
- In non-uniform circular motion, angular acceleration is constant, so tangential acceleration is constant, and the magnitude of velocity varies with time.
- In non-uniform circular motion, the normal acceleration is greater at larger radii.
- If the angle between total acceleration and velocity is acute, the motion is accelerated.
True or False
- An object in free fall increases its speed by 0.9 m/s each second. False (9.8 m/s)
- Displacement always equals distance in straight-line motion. False
- Average velocity is always tangent to the trajectory. False
- Instantaneous velocity is always tangent to the path. True
- Distance is greater than displacement magnitude in curved paths. True
- Average speed equals velocity magnitude in curved paths. False
- Curvilinear motion is accelerated. True
- Constant speed in curved paths means zero total acceleration. False
- If velocity varies only in magnitude, total acceleration is tangential. True
- If speed and acceleration are at a 45° angle, normal and tangential acceleration magnitudes are equal. True
- Instantaneous displacement indicates instantaneous velocity direction. True
- Tangential acceleration is constant and non-zero in uniform rectilinear motion. False
- Total acceleration is constant in uniformly varied rectilinear motion. True
- A horizontal position vs. time graph means zero velocity. True