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    Science  10:  Physics!

What is acceleration? What  is  acceleration?  Turn  to  your  neighbour  and  see  if  you  can  come  up  with  a  definition:      What  would  you  need  to  know  in  order  to  measure  acceleration?    List  here:        Acceleration  is  the  rate  of  change  in  velocity.      Velocity  and  acceleration  are  vectors,  so  we  need  to  include  the  magnitude  of  the  change  in  velocity  of  the  moving  object  and  indicate  the  change  in  direction  of  the  object’s  velocity.    The  object  with  the  greater  acceleration,  changes  its  velocity  in  a  shorter  time  interval  or  has  greater  change  in  velocity  during  the  same  time  interval.  Change  velocity  faster  =  greater  acceleration.    Positive  or  negative  acceleration?    Driving  a  car  in  the  positive  direction…  When  the  car’s  speed  is  increasing,  the  car  has  a  positive  acceleration.  When  the  car’s  speed  is  decreasing,  the  car  has  a  negative  acceleration.    

Positive and Negative AccelerationWhenever the velocity of an object changes, its motion isnot uniform, and we say that the object is accelerating.Acceleration occurs when the speed of an object changes,or its direction of motion changes, or both.

Positive accelerationWhen you think of acceleration, you probably think ofsomething speeding up. However, an object that isslowing down is also changing its velocity and thereforeis accelerating. In straight-line motion, acceleration canbe either positive or negative.

Imagine you are driving along a straight, level road at 40 km/h. Sinceyour velocity is constant, you are travelling with a relatively uniform motionand passengers in your car will be experiencing a smooth ride. If you need to speed up to 60 km/h, you must press on the accelerator pedal(Figure 9.6). Suppose the forward motion of the car is represented aspositive (!). When the car’s speed is increasing, the car has a positiveacceleration.

Negative accelerationIf you need to slow down, you press on the brake pedal (Figure 9.6).Again, suppose the forward motion of the car is represented as positive (!).When the car’s speed is decreasing, the car has a negative acceleration.

Acceleration is the rate of change in velocity. Therefore, the directionof the acceleration is the same direction as the change in velocity. If anobject’s acceleration is in the same direction as its velocity, the object’sspeed increases (Figure 9.7A). If the acceleration is in an oppositedirection to its velocity, the object’s speed decreases (Figure 9.7B).Acceleration that is opposite to the direction of motion is sometimescalled deceleration (Figure 9.8 on the next page).

Chapter 9 Acceleration is the rate of change in velocity. • MHR 385

Figure 9.6 A more common name forthe accelerator pedal is the gas pedal.

brake pedal accelerator pedal

If forward motion is represented aspositive, the speed of this car is decreasingso the car has negative acceleration (B).

If forward motion is represented as positive,the speed of this car is increasing so thecar has positive acceleration (A).

Figure 9.7 The speed of both cars is changing, so they are both accelerating.

acceleration

velocity

acceleration

velocity

A B

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   If  a  car  is  driving  forward  and  increases  its  velocity  from  +2  m/s  to  +6  m/s.    If  forward  motion  is  positive,  then  the  change  in  velocity  is  +  4  m/s.      If  forward  motion  is  positive,  then  the  change  in  velocity  is  positive.  

  If  a  car’s  velocity  as  it  travels  backward  changes  from    –  1m/s  to  –  4  m/s,  the  change  is  velocity  is    –  3  m/s.      If  a  car  is  increasing  its  speed  going  backwards  then  the  velocity  is  negative  and  the  change  in  velocity  is  negative.  

 

386 MHR • Unit 3 Motion

DirectionPositive (!) and negative (") acceleration are also dependent upon thedirection of an object’s motion. Suppose a car driving forward increasesits velocity from 2 m/s to 6 m/s (Figure 9.9A). If forward motion ispositive (!), then the change in velocity would be !4 m/s. Because thechange in velocity is positive (!), which represents forward, theacceleration must also be forward.

Suppose that a different car is increasing its speed going backward(Figure 9.9B). If we define forward motion as positive (!), thenbackward motion must be negative ("). If the car’s velocity as it travelsbackward changes from "1 m/s to "4 m/s, the change in velocitywould be "3 m/s. Because the change in velocity is negative ("), whichrepresents backward, the direction of the change in velocity, andtherefore acceleration, must also be backward.

Figure 9.9A Since the carspeeds up in a forwarddirection, its sign ispositive (!).

Figure 9.9B Since the carspeeds up in a backwarddirection, its sign isnegative (").

Find out more about theeffects of acceleration onthe human body. Startyour search atwww.bcscience10.ca.

Conduct an Investigation 9-1Don page 388

Suggested Activity

Figure 9.8 A parachute reduces the landing run of a space shuttle, reducing wear on the brakes andproviding increased directional stability.

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386 MHR • Unit 3 Motion

DirectionPositive (!) and negative (") acceleration are also dependent upon thedirection of an object’s motion. Suppose a car driving forward increasesits velocity from 2 m/s to 6 m/s (Figure 9.9A). If forward motion ispositive (!), then the change in velocity would be !4 m/s. Because thechange in velocity is positive (!), which represents forward, theacceleration must also be forward.

Suppose that a different car is increasing its speed going backward(Figure 9.9B). If we define forward motion as positive (!), thenbackward motion must be negative ("). If the car’s velocity as it travelsbackward changes from "1 m/s to "4 m/s, the change in velocitywould be "3 m/s. Because the change in velocity is negative ("), whichrepresents backward, the direction of the change in velocity, andtherefore acceleration, must also be backward.

Figure 9.9A Since the carspeeds up in a forwarddirection, its sign ispositive (!).

Figure 9.9B Since the carspeeds up in a backwarddirection, its sign isnegative (").

Find out more about theeffects of acceleration onthe human body. Startyour search atwww.bcscience10.ca.

Conduct an Investigation 9-1Don page 388

Suggested Activity

Figure 9.8 A parachute reduces the landing run of a space shuttle, reducing wear on the brakes andproviding increased directional stability.

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Change  in  velocity    Change  in  velocity  is  calculated  by  subtracting  the  initial  velocity  from  the  final  velocity.    Δv  =  vf  -­‐  vi    Part  1:  You  are  riding  a  bicycle.    Give  an  example  in  words,  and  with  numbers,  of      (a)  a  positive  change  in  velocity  You  are  riding  a  bicycle  travelling  forward  at  6  m/s.    You  are  late,  so  you  increase  your  velocity  to  9  m/s  forward.  Δv  =  vf  -­‐  vi   =  +  9  m/s  –  (  +  6  m/s)       =  +  3  m/s  You  are  speeding  up  by  3  m/s  in  the  original  direction.    Your  initial  forward  direction  is  positive,  so  your  change  in  velocity  is  positive  when  you  speed  up.    (b)  a  negative  change  in  velocity  You  are  riding  a  bicycle  forward  at  9  m/s,  you  slow  down  to  2  m/s.  Δv  =  vf  -­‐  vi   =  +  2  m/s  –  (  +  9  m/s)       =  -­‐7  m/s  You  are  slowing  down  by  7  m/s  in  the  original  direction.    Your  initial  forward  direction  is  positive,  so  your  change  in  velocity  is  negative  when  you  slow  down.    (c)  constant  velocity  If  your  initial  and  final  velocities  are  equal,  your  change  in  velocity,  Δv,  would  be  zero.    Part  2:  Using  your  examples  from  part  1,  find  the  acceleration  if  the  change  in  velocity  occurred  in  a  10  s  time  interval.    a  =  Δv/Δt    a)             b)           c)      Determining  motion  from  a  velocity-­‐time  graph        

 

Chapter 9 Acceleration is the rate of change in velocity. • MHR 395

Time (s)

Velo

city

(m/s

[nor

th])

0 t 1 t 2 t 3

Velocity vs. Time

Figure 9.12 The graph shows motion with positiveacceleration (0 to t1), zeroacceleration (t1 to t2), andnegative acceleration (t2 to t3).

Determining Motion from a Velocity-Time GraphFigure 9.12 represents the motion of a school bus that has three differentmotions with uniform acceleration. Table 9.2 summarizes the motiondepicted by the graph.

Assume that the positive direction has been chosen to be north. Noticethe following information shown on the graph.– During the time interval 0 to t1, the school bus has a constant

positive acceleration, which indicates that it increases its velocity [N]at a constant rate.

– From t1 to t2, the school bus has a zero acceleration, which indicatesthat it maintains a constant velocity [N]. In other words, the schoolbus heads north with a constant speed.

– During the time interval t2 to t3, the school bus has a constantnegative acceleration, which indicates that it uniformly decreases itsvelocity [N] until it stops. During this negative acceleration, thepassengers are still moving forward while slowing down.

– During the complete 0 to t3 time interval, the school bus has beenmoving north, and therefore its final displacement would be northfrom where it started.

Reading Check1. What does the slope of a velocity-time graph represent?2. State what a straight line on a velocity-time graph indicates about:

(a) an object’s change in velocity (b) an object’s acceleration

Table 9.2 Motion of a School Bus

Time interval 0 to t1 t1 to t2 t2 to t3

Acceleration Positive [N] Zero Negative [S]

Velocity Starts from rest Travels north at Slows down to a and increases speed a constant speed stop at a constantat a constant rate rate while stilltravelling north travelling north

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Chapter 9 Acceleration is the rate of change in velocity. • MHR 395

Time (s)

Velo

city

(m/s

[nor

th])

0 t 1 t 2 t 3

Velocity vs. Time

Figure 9.12 The graph shows motion with positiveacceleration (0 to t1), zeroacceleration (t1 to t2), andnegative acceleration (t2 to t3).

Determining Motion from a Velocity-Time GraphFigure 9.12 represents the motion of a school bus that has three differentmotions with uniform acceleration. Table 9.2 summarizes the motiondepicted by the graph.

Assume that the positive direction has been chosen to be north. Noticethe following information shown on the graph.– During the time interval 0 to t1, the school bus has a constant

positive acceleration, which indicates that it increases its velocity [N]at a constant rate.

– From t1 to t2, the school bus has a zero acceleration, which indicatesthat it maintains a constant velocity [N]. In other words, the schoolbus heads north with a constant speed.

– During the time interval t2 to t3, the school bus has a constantnegative acceleration, which indicates that it uniformly decreases itsvelocity [N] until it stops. During this negative acceleration, thepassengers are still moving forward while slowing down.

– During the complete 0 to t3 time interval, the school bus has beenmoving north, and therefore its final displacement would be northfrom where it started.

Reading Check1. What does the slope of a velocity-time graph represent?2. State what a straight line on a velocity-time graph indicates about:

(a) an object’s change in velocity (b) an object’s acceleration

Table 9.2 Motion of a School Bus

Time interval 0 to t1 t1 to t2 t2 to t3

Acceleration Positive [N] Zero Negative [S]

Velocity Starts from rest Travels north at Slows down to a and increases speed a constant speed stop at a constantat a constant rate rate while stilltravelling north travelling north

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