Motion
Section: Motion, Forces & Energy | Syllabus: Cambridge AS Level Physics 9702
Speed Speed tells us how fast an object is moving - how much distance it covers per unit of time. Speed Distance travelled per unit time. v = s / t v = speed (m/s) | s = distance (m) | t = time (s) The equation can be rearranged to find distance or time: s = v × t (distance = speed × time) t = s / v (time = distance ÷ speed) Worked Example: Finding Speed A cyclist completes a 1500 m stage of a race in 37.5 s.
What is her average speed? v = s / t = 1500 / 37.5 = 40 m/s Worked Example: Finding Distance A spacecraft orbits at a steady speed of 8.0 km/s. How far does it travel in 5000 s? s = v × t = 8.0 × 5000 = 40 000 km Velocity Velocity Speed in a given direction.
Velocity is a vector quantity - it has both magnitude (size) and direction. For example: "20 m/s" is a speed, but "20 m/s due north" is a velocity. Speed is a scalar quantity (magnitude only). Velocity is a vector quantity (magnitude and direction).
An object can have a constant speed but a changing velocity if its direction changes (e.g. a car going around a bend). Average Speed When speed varies during a journey, we use the average speed : Average Speed average speed = total distance travelled / total time taken This gives the overall speed of the whole journey, even if the object was speeding up or slowing down along the way.
Worked Example: Average Speed A runner completes a 400 m race in 50 s. Her speed varied throughout - she sped up at the start and slowed slightly at the end. average speed = 400 / 50 = 8 m/s This is her average - her instantaneous speed at any moment may have been higher or lower.
Speed vs Average Speed The equation v = s/t gives the instantaneous speed when used over a very short time interval, or the average speed when used over the whole journey. The syllabus uses both - always check what the question is asking for.
Distance–Time Graphs A distance–time graph shows how the distance of an object from a reference point changes over time. The shape of the graph tells us about the object's motion. Shape of Graph What it means Horizontal line (flat) Object is at rest - distance not changing Straight line sloping upward Object moving at constant speed - equal distances in equal times Curve getting steeper Object is accelerating - speed increasing Curve getting less steep Object is decelerating - speed decreasing Figure: Distance–Time Graph Shapes Four distance–time graphs shown side by side, each with distance (m) on the y-axis and time (s) on the x-axis.
Graph 1 (At rest): a completely horizontal line - distance stays constant. Graph 2 (Constant speed): a straight diagonal line with a steady gradient - equal distance covered in equal time. Graph 3 (Accelerating): a curved line that gets progressively steeper - the gradient (speed) is increasing.
Graph 4 (Decelerating): a curved line that gets progressively less steep - the gradient (speed) is decreasing. Calculating Speed from the Gradient The gradient (slope) of a distance–time graph equals the speed of the object: speed = gradient = vertical rise / horizontal run = Δs / Δt Worked Example: Speed from Gradient A car's distance–time graph shows a straight section from (0.4 h, 10 km) to (1.8 h, 90 km).
gradient = (90 − 10) / (1.8 − 0.4) = 80 / 1.4 = 57 km/h Figure: Calculating Gradient on a Distance–Time Graph A distance–time graph showing a straight-line section. A right-angled triangle is drawn under the line.
The vertical side of the triangle is labelled "Δs = change in distance (e.g. 80 km)" and the horizontal side is labelled "Δt = change in time (e.g. 1.4 h)". The gradient calculation is shown: speed = Δs / Δt = 80 / 1.4 = 57 km/h.
The triangle must be drawn as large as possible across the straight section for accuracy. Exam Tip To find the gradient, draw the largest possible right-angled triangle along the straight section and read the values from the axes - do not measure with a ruler on the page.
Speed–Time Graphs A speed–time graph shows how the speed of an object changes over time. Always check the axis labels - a speed–time graph has speed on the vertical axis and time on the horizontal axis .
Shape of Graph What it means Horizontal line at zero Object is at rest Horizontal line above zero Object moving at constant speed (zero acceleration) Straight line sloping upward Object accelerating at a constant rate Straight line sloping downward Object decelerating at a constant rate Curve (supplement) Changing acceleration - the gradient itself is changing Figure: Speed–Time Graph for a Train Journey A speed–time graph with four labelled sections.
Section A (0 to 20 s): a straight line rising from 0 to 20 m/s - constant acceleration (speeding up). Section B (20 to 50 s): a horizontal line at 20 m/s - constant speed. Section C (50 to 70 s): a straight line falling from 20 m/s to 0 - constant deceleration (slowing down).
Section D (70 to 80 s): horizontal line at zero - stationary. Each section is labelled. A note states: "Curved lines in sections A or C would indicate cha…
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