Speed, Distance, Time, Velocity Formulas Quarter 1

Speed Comparison of time and distance Three ways to calculate speed: Distance traveled per unit time Three ways to calculate speed: Average speed - Rate of motion calculated by dividing the distance traveled by the amount of time it takes to travel that distance Constant speed - Speed that does not change Instantaneous speed - Speed of an object at any given time

Calculating Speed Given Distance & Time Divide Distance by Time Distance ÷ Time = Speed Speed = Distance ÷ Time

Calculating Distance Given Speed & Time Multiply Speed and Time Distance = Speed X Time Speed X Time = Distance

Calculating Time Given Distance and Speed Divide Distance by Time Distance ÷ Speed = Time Time = Distance ÷ Speed

Example 1 Speed = distance ÷ time Speed = 300km ÷ 6 hours A car travels 300km in 6 hours. What is the speed of the car? Speed = distance ÷ time Speed = 300km ÷ 6 hours Speed = 50km/hr

Example 2 How far can a plane travel if it flies 800km/hr for 9 hours? Distance = Speed ▪ Time D = 800km ▪ 9hrs hr D = 7,200 km

Example 3 How long does it take a ship to go 500 km if it travels at a speed of 50km/hr? Time = Distance ÷ Speed T = 500 km ÷ 50 km/hr T = 10 hr

Velocity

Velocity Measures a change in position over a period of time AND in a certain direction Uses the SAME formula as speed Example 4: A plane traveling from Los Angeles to Atlanta is traveling 2000 miles in 4 hours, what is its velocity?

Velocity = Distance ÷ Time Example 4 A plane traveling from Los Angeles to Atlanta is traveling 2000 miles in 4 hours, what is its velocity? Velocity = Distance ÷ Time V = 2000 mi ÷ 4 hours V = 500 mph East

Distance-time graphs

Distance-Time Graph Graph that represents the time it takes an object to go a specific distance (speed). Time is ALWAYS on the x-axis Distance is ALWAYS on the y-axis Constant speed will be indicated with a horizontal line on a speed time graph. Decreased speed is indicated when the line slants down. Increased speed is indicated when the line slants up.

Interpret The Graph Below:

Interpret The Graph Below: The graph shows an object which is not moving (at rest). The distance stays the same as time goes by because it is not moving.

Interpret The Graph Below:

Interpret The Graph Below: The graph shows that the objects distance increases as time passes. The object is moving and so it has velocity. The straight line shows it is a constant (not changing).

Interpret The Graph Below:

Interpret The Graph Below: Just like the previous graph, this graph shows an object moving with constant velocity

Interpret The Graph Below:

Interpret The Graph Below: The curve in the graph shows that the objects velocity is changing as time passes. This is acceleration.

Interpret The Graph Below:

Interpret The Graph Below: In the first part of the graph the object is moving with constant velocity. In the second part of the graph the object is at rest (not moving). In the third part the object is again moving with constant velocity.

Interpret The Graph Below:

Interpret The Graph Below: The graph shows that the objects velocity does not change as time passes. It shows constant velocity.

Interpret The Graph Below:

Interpret The Graph Below: The graph shows that the objects velocity is increasing as time passes – it is accelerating. The straight line shows that it is constant acceleration.

Velocity-Time Graphs

Acceleration

Acceleration Measures the change in an object’s velocity over time Units include a distance and a time squared Ex: mi/hr2, m/s2

Types of Acceleration: Same Direction of Motion AKA “Speeding Up” + = A force is applied in the same direction causing the bike to speed up.

Types of Acceleration: Opposite Direction of Motion AKA “Slowing Down” + = A force is applied in the opposite direction causing the bike to slow down.

Types of Acceleration: At angle to motion AKA “Turning” + = A force is applied at an angle causing the bike to change direction. The speed may not change!

Calculating Acceleration Must know: Final velocity (speed) Initial velocity (speed) Time A = velocity final – velocityinitial time