Calculating Acceleration Unit 9.2

m/s2 average acceleration

Dv Dt a = 50 m/s – 25m/s = 4s – 2s = 12.5 m/s2

B C A A C none B

nf – ni tf – ti

Practice: A pool ball travelling at 2 Practice: A pool ball travelling at 2.5 m/s towards the cushion bounces off at 1.5 m/s. If the ball was in contact with the cushion for 0.20 s, what is the ball’s acceleration? (Assume towards the cushion is the positive direction.) = - 20. m/s2

Dv vf - vi Dt Dt a = = vf = aDt + vi = (3.0m/s2)(5.0s) + 0m/s Practice: A car accelerates from rest at 3.0 m/s2 forward for 5.0 s. What is the velocity of the car at the end of 5.0 s? Dv vf - vi Dt Dt a = = vf = aDt + vi vi = 0 m/s Dt = 5.0s a = 3.0 m/s2 vf = ? = (3.0m/s2)(5.0s) + 0m/s = 15 m/s [forward]

Dv vf - vi Dt Dt a = = Dt = vf - vi a = -22m/s – (-14m/s) -0.50m/s2 Practice: A train is travelling west at 14 m/s. How long would to increase its velocity to 22 m/s west, if it accelerated at 0.50 m/s2 west? Assign east direction positive (+). Dv vf - vi Dt Dt a = = Dt = vf - vi a = -22m/s – (-14m/s) -0.50m/s2 vi = -14 m/s vf = -22 m/s a = -0.50 m/s2 Dt = ? = 16 s

Dv vf - vi Dt Dt a = = = -18m/s – 0 m/s 4.5 s = - 4.0 m/s2 vi = 0 m/s Practice: Solve the following problems. A truck starting from rest accelerates uniformly to 18 m/s [W] in 4.5 s. What is the truck’s acceleration? Dv vf - vi Dt Dt vi = 0 m/s vf = -18 m/s Dt = 4.5 s a = ? a = = = -18m/s – 0 m/s 4.5 s = - 4.0 m/s2

Dv vf - vi Dt Dt a = = vf = aDt + vi = (-0.40m/s2)(10s) + 5.0m/s Practice: Solve the following problems. A toboggan moving 5.0 m/s forward decelerates backward at -0.40 m/s2 for 10 s. What is the toboggan’s velocity at the end of the 10 s? vi = 5 m/s a = -0.40 m/s2 Dt = 10 s vf = ? Dv vf - vi Dt Dt a = = vf = aDt + vi = (-0.40m/s2)(10s) + 5.0m/s = 1 m/s

Dv vf - vi Dt Dt a = = Dt = vf - vi a = -26m/s – (-12m/s) -3.5m/s2 Practice: Solve the following problems. How much time does it take a car travelling south at 12 m/s to increase its velocity to 26 m/s south if it accelerates at 3.5 m/s2 south? Dv vf - vi Dt Dt a = = Dt = ? vi = -12 m/s vf = -26 m/s a = -3.5 m/s2 Dt = vf - vi a = -26m/s – (-12m/s) -3.5m/s2 = 4.0 s

Air resistance same rate 9.8 m/s2 -9.8 m/s2

decreasing increasing -9.8 m/s2 -9.8 m/s2 -9.8 m/s2 A → B B B → C Velocity Acceleration decreasing increasing -9.8 m/s2 -9.8 m/s2 -9.8 m/s2

Practice: Solve the following problems. Suppose a rock falls from the top of a cliff. What is the change in velocity of the rock after it has fallen for 1.5 s? Assign “down” as negative (-). What is the change in velocity of a brick that falls for 3.5 s?

Practice: Solve the following problems. A ball is thrown straight up into the air at 14 m/s. How long does it take for the ball to slow down to an upward velocity of 6.0 m/s? A rock is thrown downwards with an initial velocity of 8.0 m/s. What is the velocity of the rock after 1.5 s?