ACCELERATION

Acceleration Acceleration is change in velocity over time. a = vf - vi If vf > vi, a is +……this is acceleration If vf < vi, a is -……this is deceleration or (-)acceleration

v vs. t graphs Slope = v/t = a What is the average acceleration over the first 40s? Area under the curve gives displacement v x t = m/s x s = m How far did the object travel in 40s?

Uniform Acceleration An object speeds up or slows down at a constant rate. Displacement depends upon initial velocity, acceleration, and time. Final velocity depends on initial velocity, acceleration and time. To solve for these unknowns, we use the 3 main Kinematics Equations

Equations using Acceleration vf = vi + at d = vit + 1/2at2 vf2 = vi2 + 2ad Be sure to use the equation that you have the most known information for and includes the variable you are looking for.

Working in 2 Dimensions When we are talking about a car or or other object traveling on the ground, we are working on the horizontal plane. We can also use these equations in a vertical plane. In a vertical plane, acceleration is due to gravity. More to come later.

Try These A car accelerates from 4m/s to 20m/s in 4s. What is the acceleration? A car starts from rest accelerates 5m/s2 over 30m. What is the final velocity of the car? A car slows from 40m/s to a stop in 5s. What is the acceleration? If an object starts from rest and accelerates 10m/s2 for 2s. How far will it travel?

Gravity

Gravity Galileo discovered that by neglecting the effects of air, all objects falling had the same acceleration. This value is “g” Or -9.8m/s2 Different places around the world have different values of g.

g g is known as the acceleration due to gravity. Because gravity accelerates objects in a downward direction, g is a negative acceleration. This is due to the fact that acceleration is a vector. GLOC

How does gravity affect things? Depends upon your reference point. If a stone drops from the top of a building: after 1 second it will be traveling -9.8m/s downward and after 2 second it will be traveling -19.6 m/s. If a ball is thrown upward gravity will slow the ball down and then the ball will accelerate back down. Time up = time down

Practice A brick is dropped from a high scaffold. What is it’s velocity after 4.0s? How far does the brick fall during this time?

More Practice A tennis ball is thrown straight up with an initial speed of 22.5m/s. It is caught at the same distance above ground. How high does the ball rise? How long did the ball remain in the air?

A ball is thrown up with an initial velocity of 29. 4 m/s A ball is thrown up with an initial velocity of 29.4 m/s. How much time does it take for the ball to stop rising?

A stone is dropped from the top of a cliff and hits the ground 3 seconds later. Find a) the magnitude of the velocity at which the stone hit the ground b) the distance that it fell.

A person standing on top of a building throws a ball downward at 5m/s A person standing on top of a building throws a ball downward at 5m/s. Find The velocity it is traveling in 3.0s The distance it travels in 3.0s