# Motion and Kinematics Key Concepts

### 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 (*v*) is_{m}**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/s**.^{2} - When an object is thrown vertically upwards, the speed decreases by
**9.8 m/s**every second while ascending.^{2}

### 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.

- In the position vs. time graph, the tangent represents
- 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**