Speed, Velocity and Acceleration

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CognitoSpeed, velocity and acceleration

Physics OnlineDistance-time and velocity-time graphs

Key facts & equations

Speed and velocity

Speed = distance / time. Units: m/s. Scalar (magnitude only).
Velocity = displacement / time. Units: m/s. Vector (magnitude AND direction).
An object can have constant speed but changing velocity (e.g. circular motion — direction changes).
Average speed = total distance / total time.
Typical speeds: walking ~1.5 m/s, cycling ~6 m/s, car ~30 m/s, sound ~340 m/s.

Acceleration

Acceleration = change in velocity / time = (v - u) / t. Units: m/s².
Deceleration = negative acceleration (slowing down).
v² = u² + 2as (Higher tier: used when time is not given).
Free fall: acceleration due to gravity g ≈ 9.8 m/s² (use 10 m/s² in estimates).
On a velocity-time graph: gradient = acceleration. Area under graph = distance.

Distance-time graphs

Gradient = speed. Steeper gradient = faster speed.
Horizontal line = stationary (zero speed).
Curved line = changing speed (acceleration or deceleration).
Slope going up = moving away from start. Slope going down = returning.

Velocity-time graphs

Gradient = acceleration. Positive gradient = accelerating. Negative = decelerating.
Horizontal line = constant velocity (zero acceleration).
Area under graph = distance travelled.
Triangles: area = ½ × base × height. Rectangles: area = base × height.

Exam questions — 4 questions · 10 marks · AQA 8463 style

3 marksCalculate accelerationAQA 8463 P1 style 🔢 Calculator

A car accelerates from 10 m/s to 30 m/s in 8 seconds. Calculate: (a) the acceleration, (b) the distance travelled using s = ut + ½at². (3 marks)

Hint: (a) a = (v-u)/t. (b) Use s = ut + ½at² with u=10, t=8, a=2.5.

+30 XP

1 markDistance-time graphAQA 8463 style

On a distance-time graph, what does a horizontal straight line represent?

A Constant acceleration

B Constant speed

C The object is stationary

D Deceleration

3 marksv-t graph areaAQA 8463 style 🔢 Calculator

A velocity-time graph shows a car travelling at 20 m/s for 5 s, then decelerating uniformly to rest over 10 s. Calculate the total distance travelled. (3 marks)

Hint: Break into two sections: rectangle (constant speed) and triangle (deceleration to zero). Area of each = distance.

+30 XP

1 markScalar vs vectorAQA 8463 style

Which of the following is a vector quantity?

A Speed

B Distance

C Mass

D Velocity

Speed, Velocity and Acceleration

Speed and velocity

Acceleration

Distance-time graphs

Velocity-time graphs

Module complete! 🎉