Tutorial 2 - Motion in 1D

PHY156/7S Tutorial 2 (Based on Ch2) Motion in 1D Question 1: Position, Velocity and Speed 1.1. 1.2. The speed of a nerve impulse in the human body is about 100 m/s. If you accidentally stub your toe in the dark, estimate the time it takes the nerve impulse to travel to your brain A particle moves according to the equation 𝑥𝑥 = 10𝑡𝑡 2 , where 𝑥𝑥 is in meters and 𝑡𝑡 is in seconds. a) Find the average velocity for the time interval from 2.00 s to 3.00 s. b) Find the average velocity for the time interval from 2.00 to 2.10 s. Question 2: Instantaneous Velocity and Speed 2.1. An athlete leaves one end of a pool of length L at 𝑡𝑡 = 0 and arrives at the other end at time 𝑡𝑡1 . She swims back and arrives at the starting position at time 𝑡𝑡2 . If she is swimming initially in the positive x direction, determine her average velocities symbolically in a) The first half of the swim b) The second half of the swim c) And the round trip. d) What is her average speed for the round trip? 2.2. A position–time graph for a particle moving along the x axis is shown in Figure P2.5. a) Find the average velocity in the time interval 𝑡𝑡 = 1.50 s to 𝑡𝑡 = 4.00 s. b) Determine the instantaneous velocity at 𝑡𝑡 = 2.00 s by measuring the slope of the tangent line shown in the graph. c) At what value of t is the velocity zero? Question 3: Analysis Model: Particle Under Constant Velocity 3.1. A car travels along a straight line at a constant speed of 60.0 mi/h for a distance d and then another distance d in the same direction at another constant speed. The average velocity for the entire trip is 30.0 mi/h. a) What is the constant speed with which the car moved during the second distance d? b) What If? Suppose the second distance d were travelled in the opposite direction; you forgot something and had to return home at the same constant speed as found in part a). What is the average velocity for this trip? c) What is the average speed for this new trip? 3.2. A person takes a trip, driving with a constant speed of 89.5 km/h, except for a 22.0-min rest stop. If the person’s average speed is 77.8 km/h, a) how much time is spent on the trip and b) how far does the person travel? Question 4: Acceleration 4.1. A child rolls a marble on a bent track that is 100 cm long as shown in Figure P2.8. We use x to represent the position of the marble along the track. On the horizontal sections from x = 0 to x = 20 cm and from x = 40 cm to x = 60 cm, the marble rolls with constant speed. On the sloping sections, the marble’s speed changes steadily. At the places where the slope changes, the marble stays on the track and does not undergo any sudden changes in speed. The child gives the marble some initial speed at x = 0 and t = 0 and then watches it roll to x = 90 cm, where it turns around, eventually returning to x = 0 with the same speed with which the child released it. Prepare graphs of x versus t, vx versus t, and ax versus t, vertically aligned with their time axes identical, to show the motion of the marble. You will not be able to place numbers other than zero on the horizontal axis or on the velocity or acceleration axes, but show the correct graph shapes. 4.2. A particle starts from rest and accelerates as shown in Figure P2.11. Determine: a) the particle’s speed at 𝑡𝑡 = 10.0 s and at 𝑡𝑡 = 20.0 s, and b) the distance travelled in the first 20.0 s. Question 5: Analysis Model: Particle Under Constant Acceleration 5.1. An electron in a cathode-ray tube accelerates uniformly from 2.00 × 104 m/s to 6.00 × 106 m/s over 1.50 cm. a) In what time interval does the electron travel this 1.50 cm? b) What is its acceleration? 5.2. A parcel of air moving in a straight tube with a constant acceleration of 24.00 m/s2 has a velocity of 13.0 m/s at 10:05:00 a.m. a) What is its velocity at 10:05:01 a.m.? b) At 10:05:04 a.m.? c) At 10:04:59 a.m.? d) Describe the shape of a graph of velocity versus time for this parcel of air. e) Argue for or against the following statement: “Knowing the single value of an object’s constant acceleration is like knowing a whole list of values for its velocity.” Question 6: Freely Falling Objects 6.1. An attacker at the base of a castle wall 3.65 m high throws a rock straight up with speed 7.40 m/s from a height of 1.55 m above the ground. a) Will the rock reach the top of the wall? b) If so, what is its speed at the top? If not, what initial speed must it have to reach the top? c) Find the change in speed of a rock thrown straight down from the top of the wall at an initial speed of 7.40 m/s and moving between the same two points. d) Does the change in speed of the downward-moving rock agree with the magnitude of the speed change of the rock moving upward between the same elevations? e) Explain physically why it does or does not agree.