Motion Along a Straight Line (AQA A Level Physics): Revision Note

Displacement, speed, velocity & acceleration

Scalar quantities

• Scalar quantities only have a magnitude (size)

  • Distance: the total length between two points

  • Speed: the total distance travelled per unit of time

Vector quantities

• Vector quantities have both magnitude and direction

  • Displacement: the distance of an object from a fixed point in a specified direction

  • Velocity: the rate of change of displacement of an object

  • Acceleration: the rate of change of velocity of an object

Equations for velocity and acceleration

• The equation for velocity is

$v=\frac{∆s}{∆t}$

• Where:

  • $v$ = velocity (m s^-1)

  • $∆s$ = change in displacement (m)

  • $∆t$ = change in time (s)

• The equation for acceleration is

$a=\frac{∆v}{∆t}$

• Where:

  • $a$ = acceleration (m s^-2)

  • $∆v$ = change in velocity (m s^-1)

  • $∆t$ = change in time (s)

Average & instantaneous speed

Instantaneous speed / velocity

• The instantaneous speed (or velocity) is the speed (or velocity) of an object at any given point in time

• This could be for an object moving at a constant velocity or accelerating

  • An object accelerating is shown by a curved line on a displacement – time graph

  • An accelerating object will have a changing velocity

• To find the instantaneous velocity on a displacement-time graph:

  • Draw a tangent at the required time

  • Calculate the gradient of that tangent

Average speed / velocity

• The average speed (or velocity) is the total distance (or displacement) divided by the total time

• To find the average velocity on a displacement-time graph, divide the total displacement (on the y-axis) by the total time (on the x-axis)

  • This method can be used for both a curved or a straight-line on a displacement-time graph

Uniform & non-uniform acceleration graphs

• Three types of graph that can represent motion are displacement-time graphs, velocity-time graphs and acceleration-time graphs

Displacement-time graph

• On a displacement-time graph:

  • The gradient (or slope) equals velocity

  • The y-intercept equals the initial displacement

  • A diagonal straight line represents a constant velocity

    • A positive slope represents motion in the positive direction

    • A negative slope represents motion in the negative direction

  • A curved line represents an acceleration

  • A horizontal line (zero slope) represents a state of rest

  • The area under the curve is meaningless

• Remember the displacement-time graph can have positive or negative values on the displacement axis

  • However, a distance-time graph only has positive values

Velocity-time graph

• On a velocity-time graph:

  • Slope equals acceleration

  • The y-intercept equals the initial velocity

  • A straight line represents uniform acceleration

    • A positive slope represents an increase in velocity (acceleration) in the positive direction

    • A negative slope represents an increase in velocity (acceleration) in the negative direction

  • A curved line represents the non-uniform acceleration

  • A horizontal line (zero slope) represents motion with constant velocity

  • The area under the curve equals the displacement or distance travelled

• Remember the velocity-time graph can have positive or negative values on the displacement axis

  • However, a speed-time graph only has positive values

Acceleration-time graph

• On an acceleration-time graph:

  • The slope is meaningless

  • The y-intercept equals the initial acceleration

  • A horizontal line (zero slope) represents an object undergoing constant acceleration

  • The area under the curve equals the change in velocity