WJEC Physics 3, Topic 6 Motion

Introduction

This topic is an extension of Topic 6 of P2, although in P3 we take a more mathematical approach. For all motion problems, we will assume acceleration is uniform, as variable acceleration is too complex for GCSE.

We will be discussing velocity in this topic. In P2 we discussed speed, which is a scalar quantity. This means it has only a magnitude. Velocity is a vector quantity. This means it has a magnitude and a direction.

Notation

a = acceleration, m/s²

u = initial velocity, m/s

v = final velocity, m/s

t = time, s

x = distance, m

Constant Acceleration

Acceleration is the measure of how quickly a velocity is changing, per unit time. If acceleration is constant, it can be defined by the following equation, where Δv is the change in velocity (v-u) and Δt is the change in time.

a= Δv ÷ Δt

This equation can be rearranged to make v the subject.

v = u + at

Example: A runner accelerates from 3m/s at 0.2m/s² for 10s. What is her final velocity?

 v = u + at

v = 3 + (0.2 × 10)

v = 10 m/s

Calculating Distance Travelled

In P2, we worked out distance by calculation the area under a velocity-time graph. There are two formulas that we can use to define distance travelled without relying upon a graph. They are;

x = ut + ½at²

x =  ½(u+v) × t

Example: A cyclist starts from rest and reaches a final velocity of 5m/s in 10s. He accelerates at 0.5m/s², calculate the distance he travels.

x =  ½(u+v) × t

x = ½(0+5) × 10

x = 25m

Example: A tourist drops a croissant from the top of the Eiffel Tower. The croissant falls for 8 seconds, calculate the height of the Eiffel Tower. Assume acceleration is 10m/s², due to gravity.

x = ut + ½at²

x = (0 × 8) + ½(10 × 8²)

x = 320m

Example: A motorcyclist brakes from 30m/s to a standstill in 5 seconds. What is the rider’s decceleration? (Note that if the value of 'a' is negative, the body is decelerating)

a= Δv ÷ Δt

a = (0 - 30) ÷ 5

a = -6m/s²

Comparing Kinetic Energy and Momentum

Both kinetic energy and momentum measure motion. Kinetic energy is a scalar quantity. It is the energy the body has due to its velocity and is calculated by the following formula;

K.E = ½mv², where m = mass (kg) and v = velocity (m/s)

Momentum is a vector quantity. It is a measure of how difficult a body is to stop and is calculated using the following formula;

p = mv, where p = momentum (kg m/s), m = mass (kg) and v = velocity (m/s)

The Effect of Mass and Velocity on Momentum

The greater the mass of a body; the greater its kinetic energy and momentum. The greater the velocity of a body; the greater its kinetic energy and momentum.

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