Acceleration

Acceleration = ∆V in m/s2 or m s-2 ∆T Acceleration is the rate of change of velocity with respect to time. Change in velocity Can be change in speed or direction Acceleration = ∆V in m/s2 or m s-2 ∆T Average acceleration = average acceleration a = Final velocity – Initial velocity Time taken v-u t

Acceleration problem A roller coaster’s velocity at the top of a hill is 10m/s. Two seconds later it reaches the bottom of the hill with a velocity of 26m/s. What is the acceleration of the roller coaster?

Acceleration = ∆V/ ∆T a = 26m/s – 10m/s 2 s a = 16m/s 2s Answer Acceleration = ∆V/ ∆T a = 26m/s – 10m/s 2 s a = 16m/s 2s a = 8m/s/s or 8m/s2 or 8 m s-2

More acceleration problems 1. A car accelerates at a rate of 20km/hr/s. How long does it take to reach a speed of 80 km/hr? 2. A car travels at 60 km per hour around a curve. Is the car accelerating? 3. A car travels in a straight line at 60km/hr. Is the car accelerating?

Answers: 1. ∆V 80km/hr a t 20km/hr/s t 4sec = t 2. yes! Because it’s changing direction! 3. no! It’s not changing speed or direction!

Deceleration Negative acceleration Example: A car slows from 60km/hr to 20km/hr in 4 seconds. What is its acceleration?

Answer: Acceleration = ∆V/ ∆T Acceleration = Vf – Vi t a = 20km/hr – 60km/hr 4 s a = -40km/hr 4s a = -10km/hr/s

Constant Acceleration If the average acceleration of a body is always the same the body has constant (uniform) acceleration. The equations of motion ón the Leaving Certificate Physics apply only objects moving in straight líne with constant acceleration. v = u + a t s = u t + ½at2 v2 = u2 + 2 a s where v = final velocity s = distance u = initial velocity a = acceleration

Velocity Time Graphs Time/s Speed m/s2 5 10 20 15 25 40 50 30 60 5 10 20 15 25 40 50 30 60 Draw a speed time graph for the data shown opposite. Find the speed after 22 s? Find the time it takes to reach a speed of 55 m/s? Find the acceleration?

Velocity time graphs Answers After 22s the speed is 44 m/s After 55 m/s the times is 27.5 s The acceleration is speed / time For 20 m/s the time is 10s therefore the acceleration is = 2m/s2 Speed m/s 10 20 30 40 50 60 0 5 10 15 20 25 30 Time/s

What does your graph look like? Constant speed will be a horizontal line on a speed time graph i.e no acceleration. If the speed decreases, the line will slant down i.e. deceleration. If the speed increases, the line will slant up i.e. Acceleration. The slope of the graph is the acceleration. The area under the graph is the distance travelled.

Understanding Velocity Time Graphs

Understanding Velocity Time Graphs No acceleration constant constant

Measuring Constant Acceleration What measurements must we make to measure acceleration? The initial velocity u The final velocity v The distance travelled s One method of doing this is using a linear air track What are some advantages of this method? The linear air track minimises friction. The light gates allow for accurate start/stop timing

Measuring Constant Acceleration

Measuring Constant Acceleration 1 What equation can we use to calculate the acceleration? v2 = u2 + 2 a s How are v (final) and u (initial) velocity calculated? u = v = What must be measured to get the distance s between the initial and final velocity? s is the distance between the light gates. What causes the acceleration of the rider? The weight (force) on the pan. Why must the air track be level? To ensure constant acceleration. (tilting cause acceleration due to gravity as well as the force due the weights. l t1 l t2

Measuring Constant Acceleration Timer t1 and t2 rider l s Weight(force)

Acceleration Due to Gravity If you drop an object it accelerates downwards due the force of gravity. This force is called the weight of the object. The speed at which an object falls is affected by air resistance. In the absence of air resistance all objects fall down with the same acceleration due to gravity. (symbol = g) On Earth the value of g = 9.8 ms-2 Show animation on acceleration due to gravity

Acceleration Due to Gravity The value of g varies from place to place on the Earth. g decreases as you move away from the Earth. On different planets other heavenly bodies g is different. Since the acceleration due to gravity is constant the equations of motion apply.

Measuring Acceleration Due to Gravity