Doc Brown's Physics exam study revision notes: This section introduces and explains how to interpret a
velocity-time graph, recognising acceleration, deceleration, or constant speed
or velocity from a velocity-time graph

This page contains online questions only. Jot down
your answers and check them against the worked out answers at the end of
the page

**
2.2a Introducing and explaining v****elocity-time
graphs and acceleration**

How do you define acceleration?

How do you interpret velocity-time
graphs?

How to do acceleration formula questions?

**Acceleration is about change in speed or
velocity of an object** and is not the same as speed or velocity.

The interpretation of the seven graphs above,
by considering the gradient - positive, negative or zero,

and their mathematical sign if the values
of acceleration (+) or deceleration (-) are used in calculations.

**acceleration is the rate of change of
velocity with time**

**acceleration = change in velocity ÷ time
taken to effect the velocity change**

**
a
**(m/s^{2})
**= Δv** (m/s)
**÷ Δt** (s) (actual numerical calculations are
dealt with further down the page)

A comparison of speed/velocity - time graphs

Graph
curves upwards, velocity is increasing (+ve), but also shows
increasing acceleration, speeding up at an increasing rate.

A comparison of speed/velocity - time graphs

Graph
is
flat, shows
constant velocity/speed (+ve), zero acceleration.

e.g. Cruise control operating in a
car.

A comparison of speed/velocity - time graphs

Graph
shows
decreasing acceleration (+ve), BUT not slowing down!, still speeding up but at a
decreasing rate.

This is observed as you pull away in a car up
to a maximum speed dictated by the speed limit.

A comparison of speed/velocity - time graphs

Graph
is
linear, shows
constant or uniform acceleration (+ve), constant rate of increasing velocity.

A comparison of speed/velocity - time graphs

Graph
is
linear, shows
constant or uniform deceleration (-ve), velocity decreasing, constant rate of deceleration.

A comparison of speed/velocity - time graphs

Graph
shows
decreasing deceleration (-ve), velocity decreasing, but decelerating at an increasingly slower rate.

A comparison of speed/velocity - time graphs

Graph
shows
increasing deceleration (-ve), velocity decreasing, but slowing down at an increasingly faster rate!

You can demonstrate this by gradually
increasing the pressure on the brake pedal of a car and bringing it to sudden
halt.

The seven graphs above illustrate of what you
might see at any point on a velocity-time graph, BUT, in reality, any
speed/velocity-time graph will be far more complicated than any one of these
simple graphs. So, you may find a graph with all seven types of gradient in just
one speed/velocity-time graph, like **the velocity-time graph below which could
represent a car journey**.

2.2b
Example questions based on velocity graph interpretation
(not involving mathematical calculations)

**
Q1** The
graph below describes the velocity profile of a car journey.

**
Q2** The
diagram below describes a rollercoaster ride (a non-graph question)

**
Q2 The sketch above illustrates the design of a roller coaster ride
on car to hold several people**.

Using the numbers (1) to (9) and comment
on energy store situations or changes ...

(a) Give two places, for the freely
moving car, where acceleration or deceleration is
taking place.

(b) At what points does the car have its
maximum GPE?

(c) At which point are you getting the
greatest increase in GPE?

(d) At which points will the car have roughly equal
amounts of KE and GPE if moving freely on it own?

(e) At which points do you get
deceleration?

(f) At which point do you get the maximum
change of KE to increase a thermal energy store?

ANSWERS explained

Notes index on
acceleration, deceleration,
velocity/speed-time
graphs

**
Keywords, phrases and learning objectives for****
acceleration and graph work**

Be able to describe, interpret and explain information from a velocity-time graphs, recognising
acceleration. deceleration, constant speed and also comment on the
moving object's kinetic energy and/or gravitational potential energy.

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Notes index on
acceleration, deceleration,
velocity/speed-time
graphs