Concept explainers
A dancer moves in one dimension back and forth across the stage. If the end of the stage nearest to her is considered to be the origin of an x axis that runs parallel to the stage, her position, as a function of time, is given by
- a. Find an expression for the dancer’s velocity as a function of time.
- b. Graph the velocity as a function of time for the 14 s over which the dancer performs (the dancer begins when t = 0) and use the graph to determine when the dancer’s velocity is equal to 0 m/s.
Trending nowThis is a popular solution!
Chapter 2 Solutions
Physics for Scientists and Engineers: Foundations and Connections
- A particle moves along the x-axis with position at time t given by x(t) = e^t cos t for 0<= t <= 2pi. Find each time t, for which the particle is at rest.arrow_forwardIf at t=0s , the object is 12m to the left of the originn, what is its position at t = 5 s? CHoices: 24 m 60 m 4 m 36 m 12 marrow_forwardA bullet is traced with a fixed ruler and flash twice witha time interval of 2 ± 0.06 ms. If the position of the bullet determined is 23.0 ± 0.5 cm firstand the position of the bullet is 37.5 ± 0.5 cm next. Calculate the speed of the bullet, V(=D/T).arrow_forward
- A blue car of length 4.52 m is moving north on a roadway (hat intersects another perpendicular roadway (Fig. P2.81, page 58). The width of the intersection from near edge to far edge is 28.0 m. The blue car has a constant acceleration of magnitude 2.10 m/s2 directed south. The time interval required for the nose of the blue car to move from the near (south) edge of the intersection to the north edge of the intersection is 3.10 s. (a) How far is the nose of the blue car from the south edge of the intersection when it stops? (b) For what time interval is any part of the blue car within the boundaries of the intersection? (c) A red car is at rest on the perpendicular intersecting roadway. As the nose of the blue car enters the intersection, the red car starts from rest and accelerates east at 5.60 m/s2. What is the minimum distance from the near (west) edge of the intersection at which the nose of the red car can begin its motion if it is to enter the intersection alter the blue car has entirely left the intersection? (d) II the red car begins its motion at the position given by the answer to pan (c), with what speed does it enter the intersection?arrow_forwardA toy frog is initially at the origin of a Cartesian coordinate system. Upon leaping, its position after a second is given by P = (5.0 cm)i + (7.0 cm)j + (3.0 cm) k What is the distance (in centimeter) traveled by the toy frog assuming straight-line motion?arrow_forwardThe equation for position x (meters) for a particle moving horizontally with a constant acceleration of a = 8.128 m/s2 when the particle was initially at rest with v0 = 0 m/s and x0 = 0 meters is in the form of a second order polynomial. The value of the constant immediately preceding the t2 in that second order polynomial equation for position x (meters) is most closely:arrow_forward
- On a spacecraft two engines fire for a time of 532 s. One gives the craft an acceleration in the x direction of ax = 4.92 m/s2, while the other produces an acceleration in the y direction of ay = 7.16 m/s2. At the end of the firing period, the craft has velocity components of vx = 3743 m/s and vy = 4808 m/s. Calculate the magnitude of the initial velocity.arrow_forwardAt time t = 16 s, the velocity of a particle moving in the x-y plane is v = 0.12i + 2.69j m/s. By time t = 16.15 s, its velocity has become -0.07i + 2.56j m/s. Determine the magnitude aav of its average acceleration during this interval and the angle θ made by the average acceleration with the positive x-axis. The angle θ is measured counterclockwise from the positive x-axis.arrow_forwardYou encounter a moving walkway that is 81 m long and has a speed of 2.1 m/s relative to the ground. How long would it take you to cover the 81 m length of the walkway if, once you get on the walkway, you immediately turn around and start walking in the opposite direction with a speed of 1.6 m/s relative to the walkway? Express your answer using one significant figure.arrow_forward
- The velocity function of a particle moving along a horizontal line is given by v(t) = ln 2 * 23t , where t ≥ 0 is in seconds. The particle is initially 2/3 units to the left of the origin. Find the position of the particle when the acceleration is equal to 6(ln 2)2 .arrow_forwardA particle P moves along the line x+y=2 in the z plane with a uniform speed 3√2 ft /sec from the point z = −5 + 7i to the point z = 10−8i. If w = 2z^(2)−3 and P′ is the image, in the plane w, of P, find the magnitude of a) the velocity and b) of the acceleration of P′ After 3 secondsarrow_forwardA toy frog is initially at the origin of a Cartesian coordinate system. Upon leaping, its position after a second is given by P = (5.0 cm)i + (70 cm)) + (3.0 cm) k What is the distance (in centimeter) traveled by the toy frog assuming straight-line motion?arrow_forward
- Glencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-HillPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning