What is the relationship between acceleration speed and time?

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2 1) What is the relationship between speed, velocity, and acceleration? 2) How do you calculate speed, velocity and acceleration? 3) How can you determine motion from a graph?

3  Average speed is calculated as distance divided by time. Equation for Average Speed Instantaneous speed is the speed at a given point in time.

4  Velocity is the speed of an object in a particular direction.  Velocity describes both the speed and the direction.  Combine velocities to determine the resultant velocity.

5 1)Which of the following examples shows a change in velocity? Remember a change in velocity can be either a change in speed or a change in the direction of motion. Briefly explain your answer. a. a car coming to a stop at a stop sign b. a book sitting on a desk c. a yo-yo in motion d. a bicyclist making a left-hand turn at exactly 15 km/h

6 2. For which of the following is the velocity constant? A.a baseball traveling away from a bat after a hit B.a bicyclist on an oval track moving at a constant speed of 15 km/h C.a helicopter hovering motionless above a fixed point on the ground D.a canoe being carried down a winding river by a steady current

7  3. Mathew takes 45 s to walk eastward along a straight road to a tore 72 m away. What is their average velocity?  v = x/t = 72 m / 45 s = 1.60 m / s eastward 4. How much time does it take for a student running at an average speed of 5.00 m/s to cover a distance of 2.00 km? Write down formula: V = x / t Manipulate equation: t = x / v Convert numbers to same units: 2.00 km = (2.00 km)(1000 m/1 km) = 2000 m Solve: t = 2000 m / 5.00 m/s = 400 seconds

8  Acceleration is the rate at which velocity changes over time.  An object accelerates if its speed, direction, or both change.

9  Acceleration is the rate at which velocity changes. Acceleration Equation (for straight-line motion) In SI units, acceleration is measured in meters per second per second (m/s/s) or m/s 2.

10 Acceleration A flowerpot falls off a second- story windowsill. The flowerpot starts from rest and hits the sidewalk 1.5 s later with a velocity of 14.7 m/s. Find the average acceleration of the flowerpot. 1. List the given and the unknown values. Given:time, t = 1.5 s initial velocity, v i = 0 m/s final velocity, v f = 14.7 m/s down Unknown: acceleration, a = ? (m/s 2 and direction)

11 3. Insert the known values into the equation, and solve. 2. Write the equation for acceleration.

12 2) In science, which of the following are examples of acceleration? a) A car speeding up? b) A car breaking for a red light? c) A car driving, down a straight road at 60 mph? d) A car driving around a curve at 60 mph? (Acceleration occurs whenever and object changes its speed or changes directions. All of the above are examples of acceleration except letter c, which is an example of constant velocity. Letter D is an example of acceleration because the car changes direction as it goes around a curve.)

13 1. A bicyclist traveling at 10 m/s applies her brakes, reducing her velocity to 5 m/s. If it takes 2 seconds to slow the bike, what is the acceleration during that period? A.–5 m/s 2 B.–2.5 m/s 2 C.0 m/s 2 D.2.5 m/s 2  Answer a = (v f – v t ) / t a =(5 m/s – 10 m/s) / 2 s a = -5 m/s / 2 s a = -2.5 m/s

14 Speed and velocity can be determined from a distance-time graph. When an object’s motion is graphed by plotting distance on the y-axis and time on the x-axis, the slope of the graph is speed. Which line to the right shows greatest speed? Answer: Cruising Jet, the one with the greatest slope or steepness.

15 Acceleration can be determined from a velocity-time graph. The slope of a velocity- time graph gives you acceleration.

16 1) In the velocity time graph to the right, is velocity increasing, decreasing or constant? (Decreasing, line is sloping down.) 2) Is acceleration increasing, decreasing or constant? (Constant, because the slope does not change.)

17 3. What is the average speed of the runner whose motion is plotted on the graph? F.1.0 m/s G.1.9 m/s H.2.4 m/s I.4.5 m/s 4. During which interval is the runner’s average speed the greatest? A.0 s to 5 s B.5 s to 10 s C.15 s to 20 s D.20 s to 25 s  Answer:  3) s = d/t = 48 m/ 25 s = 1.9 m/s  4) C, greatest slope here.

18 1) Speed (B) 2) Velocity (A, D) 3) Acceleration (C) ** one will have 2 definitions. A. Speed in a particular direction B. Change in distance over time C. The change in velocity over time D. The change in displacement over time

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Speed vs Acceleration

Speed and acceleration are entirely different concepts. Every movable object is associated with motion which is measured in terms of speed. When an object starts moving, its speed is zero in the beginning, and it increases with time due to acceleration. If the body achieves a constant speed, then the acceleration ceases to exist.

Speed

Speed is defined as the rate of change of the position of a body. Thus it may be understood as distance covered by the body in a unit time. So speed may be expressed as:

Speed = Distance/Time

If “d” is the distance covered by a body in time “t,” then its speed “s” is:

s = d/t

If the distance is measured in meters and time in seconds, then the unit of speed will be meters per second.

Speed is a scalar quantity as it has only magnitude and not any specific direction. Related to speed is another term of velocity.

As already mentioned, speed has no specific direction and so it is a scalar quantity. If speed has specific direction, then it is termed as velocity. Thus velocity has magnitude as well as direction.

If a car is moving in a circle, it will have speed, but its velocity will be zero as there is no change of direction.

Acceleration

Acceleration is defined as the rate of change of velocity. So acceleration is the change in velocity per unit time. If a body has uniform velocity, its acceleration is zero. For a body to have acceleration, there must be a change in its velocity. Thus:

Acceleration = Velocity/Time

If “v” is the velocity of the body and “t” is the time taken by the body to achieve the velocity “v,” then its acceleration “a” may be understood as:

A = v/t

If the unit of velocity is in meters per second and the time is in seconds, then the unit of acceleration will be meters per second squared.

Taking the example of the car, if it is moving in a circle, the change in velocity is not there, but the direction of motion is changing and so acceleration is there.
Summary:

Speed is the distance covered in a unit of time while acceleration is the rate of change of speed.
The unit of speed in the metric system is meters per second (m/s) while that of acceleration is meters per second squared (m/s2). Speed is a scalar quantity while acceleration is a vector quantity.

Speed is related to the rate of motion while acceleration is related to the rate of motion as well as the direction of motion.

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