Speed, velocity and acceleration

1Both Mr Rabbit and Mr Tortoise took the same round trip, but Mr Rabbit slept & returned later.

Who is right? Me, as I spent less time on the trip. No, I travelled more distance every second I ran. Who runs faster?

2Some kid is lost in the woods. (a)If he walks at a speed of 4 km/hr, try to locate his possible positions on the map.

2Some kid is lost in the woods. (b)What else is important to find the kid? The direction in which he has been walking.

Reference Points

All Motion is relative All motion is relative to a reference. This means that we describe motion of an object relative to some other object

All Motion is relative In our environment, the reference for motion is the earth’s surface, and speeds are measured relative to the earth The earth moves at 107,000 km/h relative to the sun

Calculating Motion and Speed

1Speed How can we describe how fast an object moves? E.g.A car on Beltway 8 travels 90 km in 1 hour. We say that the car travels at a speed of 90 km/hr.

1Speed Speed is a measure of how fast something moves. Speed = distance travelled per unit of time SI unit: m/s or km/h (for long distances) How can we describe how fast an object moves?

and speeds up again to 60 km/. aAverage speed Its average speed over the whole journey overall distance travelled total time of travel slows down to 0 km/h, A car travels at 50 km/h, 1Speed =

Question 1 A bug crawls 10 cm in 5 sec. What was the bug’s approximate speed in cm/sec? 2 cm/sec

Average speed does not tell the variations during the journey. On most trips, the speed at any instant is often different from the average speed. aAverage speed 1Speed

bInstantaneous speed = speed at any instant Instantaneous speed 1Speed The word ‘speed’ alone  instantaneous speed Instantaneous speed  distance travelled in an extremely short time interval

Speedometer tells the car’s speed at any instant! 1Speed bInstantaneous speed

Question 2 ( ) Average speed = s = 9.53 m/s 100 m The world record for women’s 100-m race is s. What is the average speed?

Velocity

2Velocity rate of change of displacement. a speed in a given direction or velocity a vector quantity direction magnitude (speed) Velocity is...

speed = 300 km/h direction = west Train engineers use speed only. aSpeed with direction 2Velocity Pilots use velocity (direction & speed). speed = 90 km/h

bAverage velocity Average velocity = overall displacement total time of travel direction of velocity = direction of overall displacement 2Velocity

Question 3 A student runs around a circular track that is 1000m in length in a time of 30 min. What is the average velocity of the student? 0 m/min If the student runs completely around the track, they are back where they began. So their overall displacement is zero.

cInstantaneous velocity The velocity at any instant is called instantaneous velocity. If a car moves at a constant velocity... … its average and instantaneous velocities have the same value. 2Velocity

Question 4 Which of these is a correct velocity? A.55 miles per hour B.15 kilometers per second C.30 meters per second east D.400,000,000 meters per hour

Acceleration

3Acceleration When an object moves faster and faster, its speed is increasing (velocity changed).

3Acceleration When an object moves slower and slower, its speed is decreasing (velocity changed).

When an object changes direction, 3Acceleration its velocity changes too.

3Acceleration Acceleration measures the change in velocity Acceleration =  velocity per unit time direction speed overall change in velocity total time taken = m/s 2 Unit: m/s/s vector quantity =

If a car accelerates at 2 m s –2, what does that mean? 3Acceleration t = 1 s v = 2 m s –1,  v = 2 m s –1 v = 0 t = 2 s v = 4 m s –1,  v = 2 m s –1 v = 6 m s –1,  v = 2 m s –1 t = 3 s 1 m t = 0 3 m 5 m

Tommy accelerates from 20 m/s at 15 sec (t 1 ) to 40 m/s at 60 sec (t 2 ). Question 5 What is his avg. acceleration between t 1 and t 2 ? Avg. acceleration = 40 m/s – 20 m/s 60s – 15 s 20 m/s 45 s = =.44 m/s 2