MOTION

4.3 Acceleration Acceleration is the rate at which your speed (or velocity) changes.

4.3 Acceleration What is the bike’s acceleration?

4.3 Acceleration Acceleration describes how quickly speed changes. Acceleration is the change in speed divided by the change in time.

4.3 Speed and acceleration An acceleration of 20 km/h/s means that the speed increases by 20 km/h each second. The units for time in acceleration are often expressed as “seconds squared” and written as s2. Can you convert this rate using conversion factors?

A strong wind increases its speed to 4 m/s in 3 s. Solving Problems A sailboat moves at 1 m/s. A strong wind increases its speed to 4 m/s in 3 s. Calculate acceleration.

= 1 m/s2 Solving Problems Looking for: …acceleration of sailboat Given: …v1 = 1 m/s; v2 = 4 m/s; time = 3 s Relationships: a = (v2 – v1)/t Solution: a = (4 m/s – 1 m/s)/ 3 s = 1 m/s2

Your Turn (#1) = 5 m/s2 Given: Relationships: a = (v2 – v1)/t Calculate the acceleration of an airplane that starts at rest and reaches a speed of 45 m/s in 9 seconds. Given: V1=0 m/s, V2 = 45 m/s, t=9s Relationships: a = (v2 – v1)/t Solution: a = (45 m/s – 0 m/s)/ 9 s = 5 m/s2

Your Turn (#2) = -2 m/s2 Given: Relationships: a = (v2 – v1)/t Calculate the acceleration of a car that slows from 50 m/s to 30 m/s in 10 seconds. Given: V1=50 m/s, V2 = 30 m/s, t=10s Relationships: a = (v2 – v1)/t Solution: a = (30 m/s – 50 m/s)/ 10 s = -2 m/s2

Practice #1 = -0.75 m/s2 Given: Relationships: a = (v2 – v1)/t While traveling along a highway, a driver slows from 24 m/s to 15 m/s in 12 seconds. What is the automobile’s acceleration? (Remember that a negative value indicates a slowing down or deceleration.) Given: V1=24 m/s, V2 = 15 m/s, t=12s Relationships: a = (v2 – v1)/t Solution: a = (15 m/s – 24 m/s)/ 12 s = -0.75 m/s2

Practice #2 = -8.9 m/s2 Given: Relationships: a = (v2 – v1)/t A parachute on a racing dragster opens and changes the speed of the car from 85 m/s to 45 m/s in a period of 4.5 seconds. What is the acceleration of the dragster? Given: V1=85 m/s, V2 = 45 m/s, t=4.5s Relationships: a = (v2 – v1)/t Solution: a = (45 m/s – 85 m/s)/ 4.5 s = -8.9 m/s2

Practice #4 = 7.5 s Given: Relationships: a = (v2 – v1)/t Solution: A car traveling at a speed of 30.0 m/s encounters an emergency and comes to a complete stop. How much time will it take for the car to stop if it decelerates at –4.0 m/s2? Given: V1=30 m/s, V2 = 0 m/s, a= -4.0 m/s2, t=?? Relationships: a = (v2 – v1)/t Solution: t = (0 m/s – 30 m/s)/ -4.0 m/s2 = 7.5 s

Practice #5 How will we solve this one? If a car can go from 0 to 60. mph in 8.0 seconds, what would be its final speed after 5.0 seconds if its starting speed were 50. mph? How will we solve this one? This is a 2-part question Solve for the Acceleration, “a” with the first part. Solve for Vf given the Vi=50mph, and the “a” you calculated.

4.3 Acceleration on speed-time graphs Positive acceleration adds more speed each second. Things get faster. Speed increases over time.

4.3 Acceleration on speed-time graphs Negative acceleration subtracts some speed each second. Things get slower. People sometimes use the word deceleration to describe slowing down.

4.3 Acceleration on position-time graphs The position vs. time graph is a curve when there is acceleration. The car covers more distance each second, so the position vs. time graph gets steeper each second.

4.3 Acceleration on position-time graphs When a car is slowing down, the speed decreases so the car covers less distance each second. The position vs. time graph gets shallower with time.

4.3 Free fall An object is in free fall if it is accelerating due to the force of gravity and no other forces are acting on it.

4.3 Free fall Falling objects increase their speed by 9.8 m/s every second, or 9.8 m/s2

4.3 Acceleration and direction A car driving around a curve at a constant speed is accelerating because its direction is changing.

4.3 Curved motion A soccer ball is an example of a projectile. A projectile is an object moving under the influence of only gravity. The path of the ball makes a bowl-shaped curve called a parabola.

4.3 Curved motion Circular motion is another type of curved motion. An object in circular motion has a velocity vector that constantly changes direction.