7. You are given the position-time relationship below (where x is in meters and t is in seconds): 1 x =t3 – 3t + 50 - a.) Find the expression for velocity. b.) Find the expression for acceleration. c.) Produce graphs of position-time, velocity-time, acceleration-time. Make sure that the x-t, v- t, and a-t graphs are drawn to scale and aligned vertically below each other. d.) Is the acceleration constant or changing with time? e.) Find: 1- The initial position, x 2- Displacement for the time interval t= [0, 60]. 3- Position at t= 25 s. 4- Average velocity for the time interval t= [0, 60]. 5- Velocity at t = 0 and at t= 25. 6- Acceleration at t=0 and at t= 25.

7. You are given the position-time relationship below (where x is in meters and t is in seconds): 1 x =t3 – 3t + 50 - a.) Find the expression for velocity. b.) Find the expression for acceleration. c.) Produce graphs of position-time, velocity-time, acceleration-time. Make sure that the x-t, v- t, and a-t graphs are drawn to scale and aligned vertically below each other. d.) Is the acceleration constant or changing with time? e.) Find: 1- The initial position, x 2- Displacement for the time interval t= [0, 60]. 3- Position at t= 25 s. 4- Average velocity for the time interval t= [0, 60]. 5- Velocity at t = 0 and at t= 25. 6- Acceleration at t=0 and at t= 25.

College Physics

10th Edition

ISBN:9781285737027

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter2: Motion In One Dimension

Section2.3: Acceleration

Problem 2.3QQ: Parts (a), (b), and (c) of Figure 2.10 represent three graphs of the velocities of different objects...

See similar textbooks

Similar questions

In Figure 2.11b, the area under the velocitytime graph and between the vertical axis and time t (vertical dashed line) represents the displacement. As shown, this area consists of a rectangle and a triangle. (a) Compute their areas. (b) Explain how the sum of the two areas compares with the expression on the right-hand side of Equation 2.16.
Which one of the following describes an object in motion? (2.1) (a) A period of time has passed. (b) Its position is known. (c) It is continuously changing position. (d) It has reached its final position.
The kinematic equations can describe phenomena other than motion through space and time. Suppose x represents a persons bank account balance. The units of x would be dollars (), and velocity v would give the rate at which the balance changes (in units of, for example, /month). Acceleration would give the rate at which v changes. Suppose a person begins with ten thousand dollars in the bank. Initial money management, leads to no net change in the account balance so that v0 = 0. Unfortunately, management worsens over time so that a = 2.5 102 /month2. Assuming a is constant, find the amount of time in months until the bank account is empty
Construct the displacement graph for the subway shuttle train as shown in Figure 2.18(a). Your graph should show the position of the train, in kilometers, from t=0 to 20 s. You will need to use the information on acceleration and velocity given in the examples for this figure.
A spacecraft lands on a newly discovered planet orbiting the star 51 Pegasi. To measure the acceleration from gravity on the planet, an astronaut drops a rock from a height of 2 m. A precision timer indicates that it takes the rock 0.71 s to fall to the surface. What is the acceleration from gravity on this planet?
A runner in a marathon passes the 5-mile mark at 1 o’clock and the 20-mile mark at 3 o clock. What is the runner’s average speed during this time period?
An object that is thrown straight up falls back to Earth. This is one-dimensional motion. (a) When is its velocity zero? (b) Does its velocity change direction? (c) Does the acceleration clue to gravity have the same sign on the way up as on the way clown?
A fireworks shell is accelerated from rest to a velocity of 65.0 m/s over a distance of 0.250 m. (a) How long did the acceleration last? (b) Calculate the acceleration.
Visualize the connection for the descriptions of motions in the sections and give answers in the blanks.
Suppose you drop a rock into a dark well and, using precision equipment, you measure the time for the sound of a splash to return. (a) Neglecting the time required for sound to travel up the well, calculate the distance to the water if the sound returns in 2.0000 s. (b) Now calculate the distance taking into account the time for sound to travel up the well. The speed of sound is 332.00 m/s in this well.
Kinematics graphs are great for showing how a quantity depends on time. For example, an acceleration-versus-time graph shows how acceleration depends on time. a. Based on your experience with two other kinematics graphs (position- and velocity-versus-time), describe how to plot an acceleration-versus-time graph. b. Describe how all three kinematics graphs are connected by slopes of tangent lines (derivatives). c. If a particles acceleration is positive and constant, what is the shape of the curve in each of the three kinematics graphs?
A student drives a moped along a straight road as described by the velocity-versus-time graph in Figure P2.12. Sketch this graph in the middle of a sheet of graph paper. (a) Directly above your graph, sketch a graph of the position versus time, aligning the time coordinates of the two graphs. (b) Sketch a graph of the acceleration versus time directly below the velocity-versus-time graph, again aligning the time coordinates. On each graph, show the numerical values of x and ax for all points of inflection. (c) What is the acceleration at t = 6.00 s? (d) Find the position (relative to the starting point) at t = 6.00 s. (e) What is the mopeds final position at t = 9.00 s? Figure P2.12