Speed, Velocity and Acceration

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

How Fast? How can you determine the average speed of each jogger?

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

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

The slope of the position-time graph on the right is –5.0 m/s. It indicates the average velocity of the object and not its speed. The slope of the position-time graph on the right is –5.0 m/s. It indicates the average velocity of the object and not its speed. The object moves in the negative direction at a rate of 5.0 m/s. Average Velocity

Average Speed The absolute value of the slope of a position- time graph tells you the average speed of the object, that is, how fast the object is moving. The sign of the slope tells you in what direction the object is moving. The combination of an object’s average speed, and the direction in which it is moving is the average velocity. If an object moves in the negative direction, then its displacement is negative. The object’s velocity will always have the same sign as the object’s displacement.

Section Check Which of the following statement defines the velocity of the object’s motion? Question 1 A. The ratio of the distance covered by an object to the respective time interval. B. The rate at which distance is covered. C. The distance moved by a moving body in unit time. D. The ratio of the displacement of an object to the respective time interval.

Section Check Answer: D Answer 1 Reason: Options A, B, and C define the speed of the object’s motion. Velocity of a moving object is defined as the ratio of the displacement (d) to the time interval (t).

Section Check Which of the statements given below is correct? Question 2 A. Average velocity cannot have a negative value. B. Average velocity is a scalar quantity. C. Average velocity is a vector quantity. D. Average velocity is the absolute value of the slope of a position-time graph.

Section Check Answer: C Answer 2 Reason: Average velocity is a vector quantity, whereas all other statements are true for scalar quantities.

The position-time graph of a car moving on a street is as given here. What is the average velocity of the car? Question 3 Section Check A. 2.5 m/s B. 5 m/s C. 2 m/s D. 10 m/s

Section Check Answer: C Answer 3 Reason: Average velocity of an object is the slope of the position-time graph.

Velocity/ time Graph The graph shows that the car’s motion is not uniform: the displacements for equal time intervals on the graph get larger and larger. The slope of a non- linear velocity-time graph will predict an objects instantaneous acceleration. a = v/t

 A constant acceleration produces a straight line on a velocity/time graph  The slope of a velocity time graph is the average acceleration. a = v/t Velocity/ Time Graphs a = v/t Slope = acceleration

Positive acceleration Negative acceleration

Acceleration = final velocity- starting velocity Acceleration = final velocity- starting velocitytime acceleration = V f - V i acceleration = V f - V it Acceleration = change in velocity =  V time t a = v/t Acceleration = Change in Velocity

Acceleration = Velocity (final) - Velocity (original) time A car traveling at 60 mph accelerates to 90 mph in 3 seconds. What is the car’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 the car’s acceleration? = 0 mph - 60 mph 6 seconds = - 60 mph 6 seconds = - 10 miles per hour per second