Motion Maps

Motion Map Parts The dot: Indicates the position of the object The arrow: indicates the direction and speed of the object. (sometimes called a vector)

Dots and Arrows Together Dot alone = not moving. Dot and arrow together: Position, direction and speed.

Direction and Size Right = positive direction Left = negative direction The longer the arrow, the greater the velocity. SLOW FASTER FASTEST

The grid…. Motion Maps are drawn along a grid to show the position of the object. Draw a minimum of 3 arrows to show a pattern. Forward, Constant Velocity, Slow Forward, Constant Velocity, Faster

More Complicated Motion… The object moves forward at constant velocity, then stops and remains in place for two seconds, then moves backward at a slower constant velocity.

Example 1 Draw a motion map. The car is accelerating! Each successive arrow is longer, indicating the velocity is increasing. Draw a motion map.

Example 2 The car is accelerating! The car is NOT moving. Each successive arrow is SMALLER, indicating the velocity is decreasing over time. The car is NOT moving. A dot indicates time is passing, but no arrow means no velocity. The car is moving at constant velocity! The arrows are all the same size, this indicates that the velocity is NOT changing.

A softball player slides into second base A softball player slides into second base. Use the particle model to draw a motion diagram of the player from the lime he begins to slide until he reaches the base. Number the dots in order, starting with zero.

A skydiver jumps out of an airplane A skydiver jumps out of an airplane. Her speed steadily increases until she deploys her parachute, at which point her speed quickly decreases. She subsequently falls to earth at a constant rate, stopping when she lands on the ground. Draw a motion diagram, using the particle model, that shows her position at successive times and includes velocity vectors.

A car travels to the left at a steady speed for a few seconds, then brakes for a stop sign. Use the particle model to draw a motion diagram of the car for the entire motion described here. Number the dots in order. starting with zero.

Reason: The initial velocity is zero Reason: The initial velocity is zero. The velocity increases and the space between position markers increases until the chute is deployed. Once the chute is deployed, the velocity decreases and the spacing between the position markers decreases until a constant velocity is obtained. Once a constant velocity is obtained, the position markers are evenly spaced. See the following figure.

Interpret the problem by drawing a motion diagram (do not solve the problem). In a typical greyhound race, a dog accelerates to a speed of 20 m/s over a distance of 30 m. It then maintains this speed. What would be a greyhound’s time in the 100 m dash?

Prepare: Since the dog accelerates for 30 m, the position dots will be successively farther apart and the velocity vectors will increase for this part of the race. After the dog reaches its top speed (at 30 m), the position dots are uniformly spaced and the velocity vectors are all the same length.

Interpret the problem by drawing a motion diagram (do not solve the problem). The giant eland, an African antelope, is an exceptional jumper, able to leap 1.5 m off the ground. To jump this high, with what speed must the eland leave the ground?

Assess: On the way up, the velocity vector decreases to zero as it should and the spacing between the position dots decreases as it should. The magnitude of the velocity vector at any position is the same on the way up as it is on the way down. This allows us to conclude that the figure is correct.

Write a one or two sentence “story” about a real object that has this motion diagram. Your story should talk about people or objects by name and say what they are doing.

A bowling ball is at rest at the top of an incline A bowling ball is at rest at the top of an incline. You nudge the ball giving it an initial velocity and causing it to roll down an incline. At the bottom of the incline it bounces off a sponge and travels back up the incline until it stops. P1.44. Prepare: Knowing the dots represent the position of an object at equal time intervals and the vectors represent the velocity of the object at these times, we can construct a situation to match the motion diagram. Solve: A bowling ball is at rest at the top of an incline. You nudge the ball giving it an initial velocity and causing it to roll down an incline. At the bottom of the incline it bounces off a sponge and travels back up the incline until it stops. Assess:The statement that you give the ball an initial velocity is consistent with the fact that the start position dot has a velocity vector. The statement that the ball rolls down the incline is consistent with the fact that the dots are getting farther apart and the velocity vectors are increasing in length. The statement that the ball bounces off a sponge is consistent with the fact that ball does not bounce back to its original position.