What we will do today Revise graphs of

What we will do today: • Revise graphs of motion (eg velocity time graphs) • Describe the motion of an acceleration-time (a-t) graph. • Draw a-t graphs from the information obtained from v-t graphs.

Velocity – time graphs • • In your jotters draw the following vt graphs: Constant velocity. Constant acceleration. Constant decelaration.

Graphs of Motion

Note that in the following graphs, a = acceleration v = velocity s = displacement Just as the area under a speed-time graph gives the distance travelled, The area under a velocity-time graph gives the displacement.

Graphs Showing Constant Acceleration a 0 v t 0 s t 0 t

Graphs Showing Constant Velocity a 0 v t 0 s t 0 t

Graphs Showing Constant Deceleration a v 0 s t 0 t

Example • a) b) The following v-t graph is produced for a moving body: Describe its movement at each point. Draw the corresponding a-t graph (values must be included).

Solution (a) AB – const accn. from 0 – 10 ms-1 in 2 s. BC – const vel. of 10 ms-1 for 2 s. CD – const decn. from 10 – 0 ms-1 in 1 s. DE – body is stationary for 3 s. EF - const accn. from 0 – 8 ms-1 in 2 s in opposite direction. FG – const vel. of 8 ms-1 for 3 s in opposite direction. GH – const decn. from 8 – 0 ms-1 in 1 s in opposite direction.

Solution (b) • BC, DE, FG – all constant vel. therefore no accn. • Use a = v – u / t for all other accn. • • AB: 10 – 0 / 2 = 5 ms-2 CD: 0 – 10 / 1 = - 10 ms-2 EF: -8 – 0 / 2 = - 4 ms-2 GH: 0 - (-8) / 1 = 8 ms-2

Solution (b)

2003 Qu: 2

2009

2008 Qu: 22(b)

2008 Qu: 22(b)

2006 Qu: 3 (A standard)

Bouncing ball • When a ball is bouncing it is constantly changing direction. • As it travels downwards it starts at 0 but accelerates due to gravity (increasing its velocity) until it hits the ground and changes direction. • As it moves upwards it has a high initial velocity that slows down to 0 at its maximum height. • A v-t graph for a bouncing ball will show motion both above and below the horizontal axis to show the constant change in direction.

Bouncing ball simulation

Example • Draw a v-t graph for the following scenario: • A girl fires a ball vertically into the air from the ground. The ball reaches its maximum height, falls, bounces and then rises to a new, lower, maximum height.

Example

Example

Example

Directions of travel • In our example we used the following: 1. Above the horizontal axis as travelling upwards 2. Below the horizontal axis as travelling downwards • Be aware that questions may also use the opposite of the above. • The key thing to remember here is that when the graph crosses the horizontal axis this means the object has changed direction ie changing from up to down.

2000 Qu: 3

2002 Qu: 2