Science 20 Physics Topic 2: Kinematic Equations

Acceleration Lanes Why is the first lane you enter on a highway called the acceleration lane? Why is it important that the lane is long enough to accommodate a wide range of possible accelerations?

Acceleration Lanes The following is a typical graph for a vehicle in an acceleration lane: Determine the initial velocity and final velocity of the vehicle in m/s and km/h. Then calculate the acceleration of this vehicle in m/s 2.

Acceleration Lanes The following is a typical graph for a vehicle in an acceleration lane: If you were travelling in another vehicle that was underpowered, the acceleration would be less than the value you just calculated. If the initial velocity and final velocity were the same, how would the shape of the graph be different?

Acceleration Lanes How would you determine the minimum length of an acceleration lane? Start by calculating the displacement of the vehicle while it accelerates!! There are 2 ways to calculate displacement 1.Remember: Displacement is the area under a velocity- time graph!! 2.Using a formula

Displacement Due to Acceleration Example 1 Step 1: divide the graph into two sections. Step 2: Calculate the area of the two sections REMEMBER: Area of a triangle = lw/2 Area of a rectangle = lw Step 3: Add the two areas together. 15m/s 5.00s

Displacement Due to Acceleration Example 1

Calculating Displacement During Accelerated Motion Example 2 A car enters the accelerated lane with an initial velocity of 65.0 km/h [E]. The car reaches a final velocity of 100.0km/h[E] in just 4.00s. Calculate the displacement of the car in meters.

Acceleration Due to Gravity The displacement equation can be used for any type of accelerated motion, like motion of objects through the air!! Remember the average acceleration near Earth’s surface is 9.81 m/s 2, directed downwards towards the planets centre.

A baseball leaves a bat and travels straight up into the air, reaching its highest point 15.9m above the bat in just 1.8s. a) Determine the initial velocity of the ball using the displacement equation Displacement Due to Acceleration Example 3

A baseball leaves a bat and travels straight up into the air, reaching its highest point 15.9m above the bat in just 1.8s. b) Determine the initial velocity of the ball using another equation Displacement Due to Acceleration Example 3

During a volleyball tournament, a player dives to prevent the ball from hitting the floor. The ball leaves the outstretched player’s arms with an initial velocity of 14.5m/s, directed straight up, and stops just below the ceiling, 10.7 m above the player’s arms. a)Calculate the time required for the ball to travel from the player’s arms to the ceiling using the displacement equation b)Calculate the time required for the ball to travel from the player’s arms to the ceiling using another equation Displacement Due to Acceleration Example 4

Passing a vehicle on a two lane highway can be scary! A car travelling 90 km/h accelerates at 0.50m/s 2 while passing another vehicle. If it takes 5.0s to pass the vehicle, determine the distance travelled by the vehicle during this time. Displacement Due to Acceleration Example 5

A car travelling 90 km/h accelerates at 0.50m/s 2 while passing another vehicle. If it takes 5.0s to pass the vehicle, determine the distance travelled by the vehicle during this time. Displacement Due to Acceleration Example 5

A car travelling 90 km/h accelerates at 0.50m/s 2 while passing another vehicle. If it takes 5.0s to pass the vehicle, determine the distance travelled by the vehicle during this time. There is another way to solve displacement problems like this that do not have a final velocity… Displacement Due to Acceleration Example 5

A car travelling 90 km/h accelerates at 0.50m/s 2 while passing another vehicle. If it takes 5.0s to pass the vehicle, determine the distance travelled by the vehicle during this time. You get the same answer either way… Displacement Due to Acceleration Example 5

Juanita leaves the surface of a trampoline with an initial velocity of 11.8 m/s, directed straight up. Determine the displacement of the gymnast after 0.80s. Displacement Due to Acceleration Example 6

A diver steps off the edge of a platform and enters the water 5.0m below. If the initial velocity of the diver was zero, determine the time it took for the diver to reach the water. Displacement Due to Acceleration Example 7

A vehicle travelling 63 km/h [E] accelerates 1.0m/s 2 [E] for 9.0 s. Determine the displacement of the vehicle during this 9.0s time interval. Displacement Due to Acceleration Example 8

Deceleration The slowing down of an object due to the acceleration vector pointing in the opposite direction as the velocity vector Usually refers to the slowing down of a vehicle If you encounter a problem that describes the motion of a vehicle moving in the positive direction as “decelerating at 4.5m/s 2,” you could translate that as negative acceleration, -4.5m/s 2.

Displacement Summary Displacement is determined by calculating the area under a velocity-time graph Displacement can also be determined by two new equations which can be rearranged to find other variables. OR

Displacement Summary If air resistance can be ignored when an object falls through the air, the object accelerates at 9.81 m/s 2 directed down towards the earth’s centre. Don’t forget to use proper sign conventions!!