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 v-t graphs: Constant velocity. Constant acceleration. Constant decelaration.

Graphs of Motion T. Ferns 6/8/04 Lo’s 1.1.8, 1.1.9

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 v s t t t

Graphs Showing Constant Velocity t

Graphs Showing Constant Deceleration v s t t t

Example 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 – 10ms-1 in 2s. BC – const vel. of 10ms-1 for 2s. CD – const decn. from 10 – 0ms-1 in 1s. DE – body is stationary for 3s. EF - const accn. from 0 – 8ms-1 in 2s in opposite direction. FG – const vel. of 8ms-1 for 3s in opposite direction. GH – const decn. from 8 – 0ms-1 in 1s 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: Above the horizontal axis as travelling upwards 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