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Forces and Motion 2.2 Introducing and explaining velocity-time graphs, acceleration and deceleration

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

INDEX for notes on acceleration, deceleration, constructing and interpreting velocity/speed-time graphs


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 velocity-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/s2) = 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.

Analyse the graph sections indicated below and describe the motion of the car at the various stages of the journey:

a-b:

b-c:

c-d:

d-e:

e-f:

f-g:

g-h:

ANSWERS explained


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

Worked out ANSWERS to the velocity-graph questions

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

Analyse the graph sections indicated below and describe the motion of the car at the various stages of the journey:

a-b: increasing acceleration,

b-c: linear/uniform/constant acceleration,

c-d: decreasing acceleration,

d-e: constant velocity, zero/no acceleration or deceleration

e-f: increasing deceleration

f-g: linear/uniform/constant deceleration,

g-h: decreasing deceleration

 

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.

At (4) and (8) car accelerating downhill, conversion of gravitational potential energy (GPE) to kinetic energy (KE).

Deceleration takes place from (5) climbing up to point (7).

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

At (3) and (7), the highest points you have the maximum in GPE, and (3) GPE > (7) GPE

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

At (1) => (2) => (3), the largest climb of the circuit.

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

The descents at point (4) and point (8), assuming half-way down.

(e) At which points do you get deceleration?

Climbing up at (6) as KE store decreases and GPE store increases.

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

Friction in the  braking zone <==(9)

 

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

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