motion
speed and velocity
speed is the distance travelled per unit time. it has no direction. velocity is speed in a given direction. it has magnitude and direction.
calculating speed
use the equation:
v = s / t
where v is speed (m/s), s is distance (m), and t is time (s).
average speed
when an object changes speed, calculate average speed using:
average speed = total distance travelled / total time taken
distance-time graphs
these graphs show how distance changes with time.
- horizontal line: object is at rest (not moving)
- straight diagonal line: object moving with constant speed
- curved line (getting steeper): object accelerating
- curved line (getting flatter): object decelerating
speed from distance-time graphs
the gradient (slope) of a straight line section equals the speed. calculate using:
speed = change in distance / change in time
speed-time graphs
these graphs show how speed changes with time.
- horizontal line: object moving with constant speed (zero acceleration)
- straight diagonal line (sloping up): object accelerating at constant rate
- straight diagonal line (sloping down): object decelerating at constant rate
- curved line: object accelerating or decelerating at changing rate
distance from speed-time graphs
the area under a speed-time graph equals the distance travelled. for constant speed or constant acceleration, use geometry to find the area (rectangle or triangle).
acceleration
acceleration is the change in velocity per unit time. use the equation:
a = Δv / Δt
where a is acceleration (m/s²), Δv is change in velocity (m/s), and Δt is time interval (s).
acceleration from speed-time graphs
the gradient (slope) of a speed-time graph equals the acceleration. a steeper line means faster acceleration.
deceleration
deceleration is negative acceleration (slowing down). when drawing speed-time graphs, a line sloping downward represents deceleration.
free fall and gravity
an object falling freely near earth's surface accelerates due to gravity. the acceleration is approximately constant:
g ≈ 9.8 m/s²
air resistance and terminal velocity
as an object falls, air resistance increases with speed. eventually, air resistance equals the weight, and the object stops accelerating. the maximum speed reached is called terminal velocity. an object falling through a liquid (like oil) reaches terminal velocity much faster than through air.
the speed-time graph for falling with air resistance shows: steep curve at first (accelerating), then flattening (approaching constant speed as terminal velocity is reached).
key equations (core and supplement)
v = s / t(speed)a = Δv / Δt(acceleration)g ≈ 9.8 m/s²(free fall)