Graphing and Acceleration 53. What's a tangent line and what is it used for? Sketch an example. 54. What is the slope of a v vs t graph for a free-falling object? Why?49.The direction of acceleration is determined by the change in velocity (Av = vf v0). Complete the following table, then invent a situation where these velocities might happen below the table. \"A\" is done for you. A) (Answer: A person at a stop-light presses the gas and goes from still (0 m/s) to 10 m/s.) 79A small stone is dropped and spends 6.0 seconds in the air until it strikes the ground. What speed is it moving when it reaches the ground? Show 7 steps. 80A cyclist, starting from rest, achieves a speed 81 82. of 15 m/s after travelling 22.5 m. What was the acceleration? Show 7 steps. .A child on a toboggan slides down a snowy hill, accelerating uniformly at 2.8 m/sZ. When the toboggan passes the first observer, it is travelling at a speed of 1.4 m/s. How fast will it be moving when it passes a second observer, who is 2.5 m downhill from the first observer? Show 7 steps. A semi-loaded train travelling at 100 m/s can decelerate at 20 m/sZ. How far in advance must the brakes be applied to come to a stop? Show 7 steps. 83A bike rider accelerates constantly to a velocity of 7.5 m/s during 4.5 s. The bike's distance is 19 m. What is the initial velocity of the bike? Show 7 steps. 65. If a car is going 100 km/hr as it passes a bystander, then passes another bystander 20 seconds later when it's going 120 km/hr, what is the car's average acceleration? Show 7 steps. 66A submarine is travelling at a constant velocity of 20 m/s for 2 hours. What distance did it travel? Show 7 steps. 67A stationary boat accelerates to 90 km/hr over 1 km. What is the time it takes to do this? Show 7 steps. 60. The motion of a race cart on a linear track is shown below. velocity (m/min) 80 60 40 20 time (min) - 20 - 40 10 20 30 40 5084. If a bullet leaves the muzzle of a rifle with a speed of 600 m/s, and the barrel of the rifle is 0.9 m long, what is the acceleration of the bullet while in the barrel? Show 7 steps. 85A baseball is popped straight up into the air and has a \"hangtime\" of 6.25 5. Determine the initial velocity of the ball. Show 7 steps. 86. If Michael Jordan has a vertical leap of 1.29 m, then what is his takeoff speed? Show 7 steps. 68A braking train can decelerate at 0.4 m/sz. If the train is travelling at 160 km/hr and needs to plan to stop at a pickup area. Howr far in advance does it need to apply the brakes? Show 7 steps. 69A satellite in space is travelling at 14 m/s in one direction. A thruster is applied for 30 s and the satellite is then travelling at 12 m/s in the opposite direction. What acceleration does the thrust cause? Show 7 steps. 70A rock is dropped off a 40-meter cliff. The rock accelerates due to gravity. What is the time it takes to hit the ground? Show 7 steps. 64. Show what happens to each of the following kinematic equations when the acceleration is zero (3:0). Once you have simplified, interpret, in words, what the equation is telling us. One equation is done for you. Dr. U\" L a) a = (example) U _U f r; t If a=0,weget0 = For this equation to be true this means that 0 = (w - v0) Or w = VD (velocity is constant is acceleration is zero) b)d = l/Gt+1/2at2 c) 11% = 1/20 + 2ad c. When is the car going in the negative direction? d. What is the fastest speed logged? Show all work. e. What is the average acceleration of the cart between 0 and 10 minutes? Show all work.75. A cross-country race car driver sets out on a 1.00 hour, 100.0 km race. At the halfway marker (50.0 km), the pit crew radios that the car had averaged a speed of only 80.0 km/h. a) How long did it take the driver to travel the first 50.0 km? Show 7 steps. b) How fast must the driver drive over the remaining distance in order to average 100.0 km/h for the entire race? Show 7 steps. 75A car starts at rest and is moving at a velocity of 25 m/s after 18 seconds. How far will it have travelled? Show 7 steps. 77A cat's displacement is 15 meters to the right in 7.0 seconds. If, at the start of the 7.0 seconds, the cat was moving at a velocity of 2.0 m/s left what was its final velocity? Show 7 steps. 78.A bus travelling at 80 km/h accelerates for 12 s to a speed of 100 km/h. What was the acceleration? Show 7 steps. 71A motorcycle is travelling at a constant velocity of 90 km/h (no acceleration). How many seconds will it take the motorcycle to cover 2 km? Show 7 steps. 72. Hikers at the bottom of a canyon are facing the canyon wall 280.5 meters away. Given that the speed of sound in air is 340 MS, how long after they shout will they hear their echo? Show 7 steps. 73A woman makes a trip to a nearby shopping mall that is located 40.0 km from her home. On the trip to the mall, she averages a speed of 80.0 km/h but gets a speeding ticket upon her arrival. On the return trip, she averages just 40.0 km/h. What was her average speed for the entire trip? Show 7 steps. 74.A car starts at rest and after 9.2 seconds is travelling at 25 m/s. How far will it have travelled during this trip? Show 7 steps. A V 50. Explain why the following misconceptions are false. a. If acceleration is zero, the object must be standing still. b. Velocity and acceleration are always the same sign (both positive or both negative). c. If speed is increasing, acceleration must be positive