Distance, Speed and Acceleration

Distance, Speed and Acceleration

AccelerationA relationship between speed and time.It is the change in speed over the change in time.a =v/tAcceleration is measured in meters per second, per second ORm/s2Basically, it is a measure of how an object is speeding up or slowing down.If the relationship between change in speed and change in time remains the same throughout the acceleration, it is called constant acceleration.When acceleration varies over a period of time, we generally describe the objects average acceleration.vav

p 384Suppose you speed up on a motorcycle from rest (0 m/s) to 9.0 m/s in a time of 2.0 s. Your change in speed is 9.0 m/s and your average acceleration is calculated as follows:v = 9.0 m/st = 2.0 sa=?aav=v/t=9.0m/s = 4.5 m/s = 4.5 m/s2 2.0 s s 4.5 meters per second squaredp 385Myriam Bedard accelerates at an average 2.5 m/s2 for 1.5 s. What is her change in speed at the end of 1.5 s?aav = 2.5 m/s2t = 1.5 sv = ?aav = v/tv = aavt = 2.5 m/s2 x 1.5 s=3.8 m/s

Bedards change in speed is 3.8 m/s.

Refining the equationIn a car, we usually know our initial speed viFrom this initial speed, we accelerate to a final speed.vfBoth the initial speed and final speed affect the change in speed.We can rewrite the equation to be more specific:

aav = v/tbecomes

p 386A skiier is moving at 1.8 m/s at the top of a hill. 4.2 s later she is travelling at 8.3 m/s. What is her average acceleration?vi = 1.8 m/st = 4.2 sv2 = 8.3 m/saav = ?a = (8.3 1.8) m/s 4.2 s

= 1.5 m/s2

RearrangingThis new equation can be rearranged to find:Initial speedFinal speedThe change in time

Graphing AccelerationA speed-time graph shows acceleration.t (s)v (m/s)002541061582010251230Time (s)Speed (m/s)

Slope and AccelerationA positive slope represents positive acceleration (speeding up).A negative slope represents negative acceleration (slowing down).No slope represents constant speed.

Area Under the LineMultiplying the two variables describes a geometric shape in the graph.From this shape, we can get an idea of the distance travelled.We can find the distance by simply finding the area under the line.Speed (m/s)Time (s)p 392, Sample problem 1A boat travels at full throttle for 1.5h. Using the graph, find the distance travelled.

p 392, Sample Problem 2Galieleo rolls a ball down a long grooved inclined plane. According to the speed-time graph, what is the distance travelled in 6.0 s?Distance-Time vs Speed-Time

Comparing GraphsDistance - timeSpeed - timeA straight positive slopeA straight positive slopeA straight horizontal lineA straight horizontal lineInstantaneous SpeedInstantaneous speed is the speed at any particular point in timeFrom a speed-time graph, we can read the instantaneous speed at any point along the line.

Constant vs Instantaneous

On a Distance-time graph, if the speed is constant then the instantaneous speed is the same at any time, and is equal to the speed and at that time.More work is required when speed is not constant.When speed is not constant:The first step is to draw a tangent across the point in time that you wish to find the speed for. You then calculate the slope for the new tangent you have drawn, giving you the instantaneous speed at that point.

Find the instantaneous speed at 2 seconds.

Find the instantaneous speed at 8 seconds.

Find the instantaneous speed at 1 second.