Speed, Velocity and Speed, Velocity and AccerationAcceration

How Fast?How Fast?

Suppose you recorded two joggers on a Suppose you recorded two joggers on a distance-time graph. How could you tell distance-time graph. How could you tell the two joggers apart on the graph?the two joggers apart on the graph?

How Fast?How Fast?

How can you determine the average speed of each jogger?

The slopes of the two lines are The slopes of the two lines are found as follows:found as follows:

Average Velocity

d dt t

f i

f i

Red slope =

6.0 m 2.0 m3.0 s 1.0 s

=

= 2.0 m/s

d dt t

f i

f i

Blue slope =

3.0 m 2.0 m3.0 s 2.0 s

=

= 1.0 m/s

The slope of a position-time graph for an object is the The slope of a position-time graph for an object is the object’s object’s average velocityaverage velocity and is represented by the and is represented by the ratio of the change of position to the time interval and ratio of the change of position to the time interval and includes the direction the object traveled.includes the direction the object traveled.

Average Velocity

t t t

f i

f i

Δ =Δd d d

v Average Velocity

• The slope of the The slope of the position-time graph position-time graph on the right is on the right is ––5.0 5.0 m/s. It indicates the m/s. It indicates the average velocity of average velocity of the object and not its the object and not its speed. speed.

The object moves in The object moves in the negative the negative direction at a rate of direction at a rate of 5.0 m/s.5.0 m/s.

Average VelocityAverage Velocity

Average SpeedThe absolute value of the slope of a position-time The absolute value of the slope of a position-time graph tells you the average speedgraph tells you the average speed of the object, of the object, that is, how fast the object is moving.that is, how fast the object is moving.

The sign of the slope tells you in what direction The sign of the slope tells you in what direction the object is moving. The combination of an the object is moving. The combination of an object’s average speed, object’s average speed, and the direction in and the direction in which it is moving which it is moving is the average velocityis the average velocity..

If an object moves in the negative direction, If an object moves in the negative direction, then its displacement is negative. then its displacement is negative. The object’s The object’s velocity will always have the same sign as the velocity will always have the same sign as the object’s displacement.object’s displacement.

v

Section CheckSection Check

Which of the following statement defines the velocity of the Which of the following statement defines the velocity of the object’s motion?object’s motion?

Question 1

A.A. The ratio of the distance covered by an object to the The ratio of the distance covered by an object to the respective time interval.respective time interval.

B.B. The rate at which distance is covered.The rate at which distance is covered.

C.C. The distance moved by a moving body in unit time.The distance moved by a moving body in unit time.

D.D. The ratio of the displacement of an object to the The ratio of the displacement of an object to the respective time interval.respective time interval.

Section CheckSection Check

Answer: DAnswer: D

Answer 1

Reason: Reason: Options A, B, and C define the speed of the Options A, B, and C define the speed of the object’s motion. Velocity of a moving object is object’s motion. Velocity of a moving object is defined as the ratio of the displacement (defined as the ratio of the displacement (dd) to the ) to the time interval (time interval (tt).).

Section CheckSection Check

Which of the statements given below is correct?Which of the statements given below is correct?

Question 2

A.A. Average velocity cannot have a negative value.Average velocity cannot have a negative value.

B.B. Average velocity is a scalar quantity.Average velocity is a scalar quantity.

C.C. Average velocity is a vector quantity.Average velocity is a vector quantity.

D.D. Average velocity is the absolute value of the slope of a Average velocity is the absolute value of the slope of a position-time graph. position-time graph.

Section CheckSection Check

Answer: CAnswer: C

Answer 2

Reason: Reason: Average velocity is a vector quantity, whereas all Average velocity is a vector quantity, whereas all other statements are true for scalar quantities.other statements are true for scalar quantities.

The position-time graph of a The position-time graph of a car moving on a street is as car moving on a street is as given here. What is the given here. What is the average velocity of the car?average velocity of the car?

Question 3

Section CheckSection Check

A.A. 2.5 m/s2.5 m/s

B.B. 5 m/s5 m/s

C.C. 2 m/s2 m/s

D.D. 10 m/s10 m/s

Section CheckSection Check

Answer: CAnswer: C

Answer 3

Reason: Reason: Average velocity of an object is the slope Average velocity of an object is the slope of the position-time graph.of the position-time graph.

f i

f i

40 m 10 m = = 2 m/s 20.0 s 5.0 s

Average velocity = = t t

v

d d

Velocity/ time GraphVelocity/ time GraphThe graph shows that The graph shows that the car’s motion is not the car’s motion is not uniform: the uniform: the displacements for equal displacements for equal time intervals on the time intervals on the graph get larger and graph get larger and larger.larger.

The slope of a non-linear The slope of a non-linear velocity-time graph will velocity-time graph will predict an objects predict an objects instantaneous instantaneous acceleration. acceleration.

a = v/ta = v/t

A constant A constant acceleration acceleration produces a produces a straight line on straight line on a velocity/time a velocity/time graphgraph

The slope of a The slope of a

velocity time velocity time graph is the graph is the average average acceleration.acceleration.

a = a = v/v/tt

Velocity/ Time Graphs

a = v/t

Slope = acceleration

PositivePositive acceleration acceleration

Negative Negative accelerationacceleration

Acceleration = Acceleration = final velocity- starting velocityfinal velocity- starting velocity

timetime

acceleration = acceleration = VVf f - V- Vii

tt

Acceleration = Acceleration = change in velocity =change in velocity = V V

timetime tt

a = a = v/v/tt

Acceleration = Change in Velocity

Acceleration =Velocity(final) - Velocity(original)

time

A car traveling at 60 mph accelerates to90 mph in 3 seconds. What is thecar’s acceleration?

=90 mph - 60 mph

3 seconds

=30 mph

3 seconds

=10 mph/second

Acceleration=Velocity(final) - Velocity(original)

time

A car traveling at 60 mph slams on the breaks to avoid hitting a deer. The car comes to a safe stop 6 seconds after applying the breaks. What is thecar’s acceleration?

=0 mph - 60 mph

6 seconds

=- 60 mph

6 seconds

=- 10 miles per hour per second