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Listed under:  Science  >  Forces and energy  >  Mechanical energy  >  Motion  >  Velocity
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EagleCat: motion graphs

Investigate distance–time and velocity–time graphs by changing position, speed and acceleration.

Interactive resource

Differential calculus: linear graphs

Observe the linear distance–time graph of a rocket travelling at a constant velocity. Calculate the average and instantaneous velocity of the rocket over different time intervals. Notice how as each time interval becomes smaller the rocket's average velocity is equivalent to its instantaneous velocity. Work out how the ...

Interactive resource

Differential calculus: non-linear graphs

Observe the non-linear distance–time graph of a rocket travelling at a changing velocity. Calculate the average and instantaneous velocity of the rocket over different time intervals. Notice how as each time interval becomes smaller, the rocket's average velocity approaches its instantaneous velocity. Use the slider to ...

Interactive resource

Differential calculus: the derivative

Observe the non-linear distance–time graph of a rocket travelling at a changing velocity. The distance, s, travelled by the rocket after t seconds is determined by the formula s(t) = t². Calculate the average velocity of the rocket over time intervals that become progressively shorter. Tabulate the results and look for ...

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Differential calculus: power functions

Observe the non-linear graphs of various power functions (such as f(x) = x², or f(x) = x³) and select the expressions for finding the gradient of the secant between small changes in x represented by Δx. Tabulate the values of f'(x) and plot the derivative of each function. Determine the pattern between the graphs for each ...

Interactive resource

Differential calculus: cubic function

Observe the non-linear distance–time graph of a rocket travelling at a changing velocity. The distance, s, travelled by the rocket after t seconds is determined by the formula s(t) = t³ – 2. Calculate the average velocity of the rocket over time intervals that become progressively shorter. Tabulate the results and look ...

Interactive resource

Differential calculus: quartic function

Observe the non-linear distance–time graph of a rocket travelling at a changing velocity. The distance, s, travelled by the rocket after t seconds is determined by the formula s(t) = t⁴ + t². Calculate the average velocity of the rocket over time intervals that become progressively shorter. Tabulate the results and look ...

Interactive resource

Differential calculus: linear and non-linear graphs

Observe the linear and non-linear distance–time graphs of a rocket travelling at both constant and changing velocities. Calculate the average and instantaneous velocities of the rocket over different time intervals. Notice what happens to the average and instantaneous velocities as the time intervals become smaller. Work ...

Interactive resource

Differential calculus: derivatives and power functions

Observe the non-linear distance-time graph of a rocket travelling at a changing velocity. Calculate the average velocity of the rocket over time intervals that become progressively shorter. Tabulate the results and derive a formula for finding the instantaneous velocity at a given point. In the second activity, observe ...

Interactive resource

Differential calculus: cubic and quartic functions

Observe the non-linear time graph of a rocket travelling at a changing velocity. The distance, s, travelled by the rocket after t seconds is determined by the formulas: s(t) = t³ – 2 and s(t) = t⁴ + t². Calculate the average velocity of the rocket over time intervals that become progressively shorter. Tabulate the results ...

Interactive resource

Physical science: fan cart physics

Experiment with the effects of force and mass on acceleration by loading fans and blocks onto a cart. For example, load a cart with three fans and turn on one fan. Monitor the displacement, velocity and acceleration as the cart moves. Analyse tables and graphs to find out how these quantities vary with time. Discover the ...

Collection

Circular motion

This collection includes six digital curriculum resources that develop the theoretical and practical aspects of circular motion. Video sequences illustrate the fundamental kinematic principles of circular motion. Reference web pages and learning objects provide background material on the mathematical techniques required, ...

Collection

Constant acceleration

This collection includes seven digital curriculum resources that develop the theoretical aspects of kinematics and equations of motion. Video sequences illustrate fundamental principles while reference web pages and learning objects provide background material on the mathematical techniques required, including calculus ...

Collection

Projectiles

This collection of six digital curriculum resources includes resources that develop the theoretical and practical aspects of projectile motion. Video sequences illustrate the fundamental kinematic principles of projectile motion and reference web pages provide background material on the mathematical techniques required, ...

Collection

Simple harmonic motion

This collection of six digital curriculum resources includes resources that develop the theoretical and practical aspects of simple harmonic motion (SHM). Video sequences illustrate the fundamental kinematic principles of SHM and reference web pages provide background material on the mathematical techniques required, including ...

Interactive resource

Constant acceleration

Learn to use your knowledge of graphs and calculus to analyse the way things move. Follow the derivation of equations to describe the position, velocity and acceleration of a moving object. Deal conceptually with both positive and negative accelerations. This resource consists of a video in three sections with animations ...

Interactive resource

Projectiles

Learn to analyse the motion of an object that is projected into the air. Look at the vertical and horizontal components of the motion. Discover how the range of a projectile depends on the angle of projection. This resource consists of a video in five sections with a supporting web page containing background material.

Interactive resource

Circular motion

Learn to use your knowledge of calculus and vectors to analyse circular motion. Follow the derivation of equations to describe angular velocity and centripetal acceleration. Discover how fast a vehicle has to travel over a hill to lose contact with the road. This resource consists of a video in four sections with a supporting ...

Interactive resource

Simple harmonic motion

Use your knowledge of calculus and circular motion to analyse back-and-forth motion. Discover how the position, velocity and acceleration vary, but are closely related. Learn how to apply the theory to vibrating objects such as pendulums and loudspeakers. This resource consists of a video in four sections with a supporting ...

Interactive Resource

Gravity and orbits

This is an interactive teaching and learning resource that years 7 to 10 secondary students can use to simulate the orbits of the Earth, Moon and a space station while altering the physical quantities involved. Orbital pathways, velocity and force vectors can be displayed in either scale or cartoon views. The mass and velocity ...