Motions and Forces

How is speed calculated?The speed of an object can be calculated using this equation:

distance travelled time takenspeed =

Speed is measured in metres per second (m/s).

Distance travelled is measured in metres (m).

Time taken is measured in seconds (s).

The standard unit for speed in physics is m/s, but other units such as kilometres per hour (km/h) are more convenient when measuring the speed of vehicles. Why is this?

Using a formula triangleA formula triangle helps you to rearrange a formula. The formula triangle for speed (s), distance (d) and time (t) is shown below.

x

Cover the quantity that you are trying to work out, which gives the rearranged formula needed for the calculation.

So to find speed (s), cover up s…

…which gives the formula…

s =d

t

What are resultant forces?There are usually several different forces acting on an object. The overall motion of the object will depend on the size and direction of all the forces.

The motion of the object will depend on the resultant force. This is calculated by adding all the forces together, taking their direction into account.

50 N 30 N

Resultant force on the crate = 50 N – 30 N

= 20 N to the left

How is GPE calculated?The GPE of an object can be calculated using this equation:

GPE = mass x gravitational field strength x height

Height is measured in metres (m).

Mass is measured in kilograms (kg).

GPE is measured in joules (j).

Gravitational field strength is measured in newtons per kilogram (N/kg), usually taken as 10 N/kg on Earth.

An osprey with a mass of 2 kg flies at a height of 200 m above the ground.

Calculating GPE question

How much gravitational potential energy does the osprey have?

= 2 x 10 x 200

GPE = mass x gravitational field strength x height

= 4,000 J

Using a formula triangleA formula triangle helps you to rearrange a formula. The formula triangle for acceleration (a), velocity (v) and time (t) is shown below.

x

Cover the quantity that you are trying to work out, which gives the rearranged formula needed for the calculation.

So to find acceleration (a), cover up a…

…which gives the formula…

a = vt

v

What’s the acceleration?What is the acceleration of the object between points A and B?

time (s)

Velo

city

(m/s

)

0 21 3 4 5 6 7 805

101520253035

A

B

the object’s velocity has increased by 20 m/s (25 - 5)

it took 4 s to change velocity (6 - 2)

acceleration = velocity /time

= 20/4

= 5 m/s2

Calculating AccelerationThe resultant force acting on an object is related to the object’s mass and acceleration. These three factors are linked by the following equation:

Resultant force is measured in newtons (N).

Mass is measured in kilograms (kg).

Acceleration is measured in metres per second per second (m/s2).

force = mass x acceleration

• A car that has a mass of 1500 kg and an acceleration of 3.0m/s2. What is the force provided by the engine?

• F = m x a

• F = 1500 kg x 3m/s2

• F = 4500 N

Example

• A formula triangle helps you to rearrange a formula. The formula triangle for acceleration (A), mass (M) and force (F) is shown below.

Formula Triangle

Using a formula triangleA formula triangle helps you to rearrange a formula. The formula triangle for acceleration (a), velocity (v) and time (t) is shown below.

x

Cover the quantity that you are trying to work out, which gives the rearranged formula needed for the calculation.

So to find acceleration (a), cover up a…

…which gives the formula…

a = vt

v

PowerPower is the rate at which work is done. It isthe amount of work per unit of time. Power (W) = Work (J) Time (S)OR Power = (Force (N) X Distance (m)). Time (s)

p

vm

p = momentum

Remember how to rearrange equations!

Remember your maths!

Scalar or vector?Velocity is a vector quantity – this means it has a magnitude (size) and direction.

Scalar quantities, such as speed, only have a magnitude.

As velocity is needed to calculate momentum, momentum must also be a vector quantity and it therefore has a direction.

A ‘+’ and a ‘-’ are often used to indicate the direction of momentum of moving objects.

6kg+ 60kg m/s

6kg - 60kg m/s