Speed-Time Graphs and Acceleration
In 2023, a Red Bull F1 car accelerated from 0 to 100 km/h in 2.1 seconds — an average acceleration of 13.2 m/s², greater than free-fall gravity.
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A car accelerates from 0 to 100 km/h in 10 seconds. Another car takes 20 seconds to reach the same speed. Which car has greater acceleration? Explain your reasoning.
Can an object be moving at constant speed and still have zero acceleration? Give a real-world example.
● Know
- Acceleration is the rate of change of velocity.
- The gradient of a speed-time graph represents acceleration.
- The area under a speed-time graph represents distance travelled.
● Understand
- Positive gradient means speeding up, negative gradient means slowing down, and zero gradient means constant speed.
● Can do
- Interpret speed-time graphs and calculate acceleration and distance from them.
Watch a traffic light turn green and count how long it takes a car to reach 60 km/h: a sports car might get there in 4 seconds, while a loaded truck might take 20 seconds. The sports car's velocity is changing far more rapidly per second — it has higher acceleration, defined as the rate of change of velocity. The formula is:
a = (v - u) / t
Where a is acceleration, v is final velocity, u is initial velocity, and t is time. Acceleration is measured in metres per second squared (m/s2).
Many students confuse acceleration with speed. Acceleration tells you how quickly speed is changing, not how fast you are going. A car sitting at traffic lights has zero speed and zero acceleration. A car cruising at 100 km/h on the highway has high speed but zero acceleration. A car that has just started moving from rest has low speed but high acceleration.
Positive acceleration means speeding up in the positive direction. Negative acceleration (deceleration) means slowing down. An object can have negative acceleration while still moving forward - it is just slowing down.
On Earth surface, objects in free fall accelerate downward at approximately 9.8 m/s2 due to gravity. This means a falling object gains about 9.8 m/s of speed every second (ignoring air resistance).
A Tesla Model 3 can accelerate from 0 to 100 km/h in about 3.5 seconds. Converting to m/s: 100 km/h = 27.8 m/s. Acceleration = 27.8 / 3.5 = 7.9 m/s2. This is about 0.8 g (where g = 9.8 m/s2). passengers feel pushed back into their seats because their bodies resist the acceleration. For comparison, a typical family car accelerates from 0-100 km/h in 8-10 seconds, giving about 0.3 g. A commercial aircraft during takeoff accelerates at about 0.2 g.
Australian vehicle safety: The Australasian New Car Assessment Program (ANCAP) tests vehicle crash safety, including acceleration during collisions. In a severe crash, deceleration can reach 50-100 g for milliseconds. Modern cars use crumple zones to extend the deceleration time, reducing peak forces on occupants. Understanding acceleration is literally life-saving in automotive engineering.
Acceleration always means going faster. This is false. Acceleration means changing velocity. If velocity is decreasing, acceleration is negative (deceleration). If velocity is constant, acceleration is zero. An object can even have acceleration perpendicular to its velocity, which changes direction without changing speed - this is what happens in circular motion.
A car accelerates from 0 to 100 km/h in 10 seconds. Then it maintains 100 km/h for 30 seconds. Then it brakes to a stop in 5 seconds. During which phase is the acceleration greatest?
How close was your prediction?
Nice calibration — your intuition is good for this kind of problem.
Good — being surprised is the point. This answer is worth remembering.
A speed-time graph provides different information than a distance-time graph. The slope of a speed-time graph represents acceleration, not speed. The area under the graph represents distance travelled.
Flat horizontal line: Constant speed, zero acceleration. The object maintains the same velocity.
Straight line going up: Constant positive acceleration. The object speeds up at a steady rate.
Straight line going down: Constant negative acceleration (deceleration). The object slows down at a steady rate.
Curved line: Changing acceleration. The rate of speed change itself changes.
The area under the graph is calculated by dividing it into simple shapes: rectangles for constant speed segments, triangles for constant acceleration segments, and combinations for more complex motion.
A train journey produces this speed-time graph: it accelerates from 0 to 20 m/s over 20 seconds (a triangle with area = 0.5 * 20 * 20 = 200 m), maintains 20 m/s for 60 seconds (a rectangle with area = 20 * 60 = 1,200 m), then decelerates to 0 over 20 seconds (another triangle with area = 200 m). Total distance = 200 + 1,200 + 200 = 1,600 metres. The average speed = total distance / total time = 1,600 / 100 = 16 m/s.
Australian rail engineering: Sydney Trains uses speed-time graphs to optimise energy consumption on the rail network. By calculating the exact acceleration and braking profiles that minimise energy use while maintaining schedule, engineers have reduced electricity consumption by 10-15%. The graphs account for track gradients, speed limits, and station spacing. This is practical physics directly improving sustainability.
A speed-time graph that goes down means the object is moving backward. This is false. The graph shows speed (a scalar) on the vertical axis, not velocity (a vector). A downward slope means the object is slowing down while still moving in the same direction. To show backward motion, you need a velocity-time graph with negative velocity values.
Newton First Law of Motion states that an object will remain at rest or move at constant velocity unless acted upon by an unbalanced force. This means that constant speed does not require force - changing speed does.
When a car moves at constant velocity on a highway, multiple forces act on it: the engine pushes forward, friction and air resistance push backward, gravity pulls down, and the road pushes up (normal force). These forces are balanced - the forward force equals the backward force, and the upward force equals the downward force. The net force is zero, so acceleration is zero.
To speed up, the driver increases engine force, making it larger than friction. The unbalanced forward force causes forward acceleration. To slow down, the driver reduces engine force or applies brakes, making backward forces larger than forward force. The unbalanced backward force causes deceleration.
This principle applies to all motion. A book on a table has balanced forces (gravity down, normal force up). A satellite in orbit has balanced forces (gravity toward Earth balanced by inertia in a curved path). Any object moving at constant velocity has balanced forces, regardless of how fast it is moving.
A skydiver jumps from a plane. Initially, gravity is the only significant force, so they accelerate downward at 9.8 m/s2. As speed increases, air resistance grows. Eventually, air resistance equals gravity - forces are balanced. The skydiver reaches terminal velocity (about 200 km/h belly-to-Earth, 320 km/h head-down) and stops accelerating. They continue falling at constant speed until the parachute opens, dramatically increasing air resistance and creating a new, much lower terminal velocity.
Australian aerospace: The Hypersonic International Flight Research Experimentation (HIFiRE) program, a collaboration between the Australian Defence Science and Technology Group and the US Air Force, studies flight at hypersonic speeds (over Mach 5). At these speeds, air resistance generates enormous heat, and the forces on the vehicle change dramatically compared to subsonic flight. Understanding force balance at extreme speeds is essential for designing hypersonic vehicles that could reduce flight times from Sydney to London to under two hours.
Objects naturally slow down and stop unless force keeps them moving. This Aristotelian view was accepted for nearly 2,000 years but is wrong. In reality, objects in motion stay in motion unless a force acts to stop them. What makes everyday objects slow down is friction and air resistance. In space, where these forces are negligible, objects continue moving indefinitely. The Voyager spacecraft launched in 1977 is still travelling at about 17 km/s, 45 years later, with no engine thrust.
1. A speed-time graph shows a straight line going up from (0, 0) to (5 s, 20 m/s). What is the acceleration? Show your working.
2. Explain how you would calculate the distance travelled by an object from a speed-time graph.
- Confusing distance-time graphs with speed-time graphs. — On a distance-time graph, gradient = speed. On a speed-time graph, gradient = acceleration and area = distance. Do not mix them up.
- Thinking that zero acceleration means the object is not moving. — Zero acceleration means constant speed. The object could be moving at a steady speed of 50 km/h with zero acceleration.
📓 Copy Into Your Books
▼Speed-Time Graph
Vertical axis = speed, horizontal axis = time. Horizontal line = constant speed. Upward slope = acceleration. Downward slope = deceleration.
Acceleration Formula
Acceleration = change in speed / change in time. Units: m/s².
Area Under the Graph
The area under a speed-time graph represents the distance travelled.
Deceleration
Deceleration is negative acceleration. It occurs when an object slows down.
You learned that speed-time graphs show how speed changes over time, with gradient representing acceleration and area representing distance.
A car travels at a constant speed of 20 m/s for 10 seconds. What is its acceleration, and what is the total distance travelled?
The hook used Formula 1 cars hitting 100 km/h in under 2.5 seconds — roughly 11 m/s², more than gravity — and described how a speed-time graph tells engineers exactly what the driver did in every corner.
Now that you can draw and interpret speed-time graphs and calculate acceleration, how would you describe an F1 car's motion through a sharp corner using the graph features you've learned? Did the racing example help you see acceleration as something more than just 'speeding up'?
1. On a speed-time graph, what does the gradient represent?
2. What does the area under a speed-time graph represent?
3. A car increases its speed from 5 m/s to 15 m/s in 4 seconds. What is its acceleration?
4. A horizontal line on a speed-time graph means:
5. Deceleration is best described as:
A cyclist accelerates from rest to 8 m/s in 4 seconds, maintains this speed for 6 seconds, then decelerates to rest in 2 seconds. Sketch the speed-time graph and calculate the total distance travelled. (3 marks)
Hint: Calculate the area under each section of the graph and add them together.
Explain the difference between a distance-time graph and a speed-time graph, including what the gradient represents in each case. (3 marks)
Hint: Compare the axes and what the slope tells you for each type of graph.
A car travelling at 30 m/s brakes and comes to rest in 5 seconds. Calculate its deceleration and explain what the negative sign means. (3 marks)
Hint: Use a = (v - u) / t, where u is initial speed and v is final speed.