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In which of these situations would the average velocity vector
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- e.g. There is a ball is sinking in some 0 with = (10m-s¹), and acceleration a = (-1.0s¯¹)v} (1) How much time does it take before it is almost stop moving? (2) How long does it pass during this period? 37arrow_forwardAn object moves in a plane from position r1=(-1,-2) m to the position r2=(-2,7 m and then to r3=(3,8)m. The time of the motion is t=30s. Find (a) total displacement; (b) distance between the initial and final positions; (c)distance travelled (d)average velocity and average speedarrow_forwardA particle travels so that its acceleration is given by 2e-ti + 5 cos tj – 3 sin t k a = If the particle is located at (1, –3, 2) at time t=0 and is moving with a velocity given by 4i – 3j+ 2k, find the magnitude of acceleration at t=0s a) 4.38 b) 5.38 c) 6.38 d)7.38arrow_forward
- Does a car moving around a circular track with constant speed have (a) zero acceleration, (b) an acceleration in the direction of its velocity, (c) an acceleration directed away from the center of its path, (d) an acceleration directed toward the center of its path, or (e) an acceleration with a direction that cannot be determined from the given information?arrow_forwardUse the definition to find an expression for the instantaneous velocity of an object moving with rectilinear motion according to the given functions relating s and t. s=³ - 81? The expression for the instantaneous velocity of the object isarrow_forwardThe position vector of a cat running on a field is given by: r(t) 312 – 4t + 2 y(t) 6t2 – 5t where x, y are in meters and t is in seconds. (a) Compute the magnitude and direction of the average velocity in the time interval betweent = 0 and t = 3 seconds. (b) Find the magnitude and direction of the acceleration of the cat at t = 2 and at t = 4 secondsarrow_forward
- (c) Find, to the nearest metre, the distance between points P and R. A car is travelling on a straight horizontal road. The velocity of the car, vms ', at time t secondsm it travels past three points, P, Q and R, is modelled by the equation -1 v = at +bt+c, where a, b and c are constants. The car passes P at time t = 0 with velocity 8 ms. (a) State the value of c. The car passes Q at time t = 5 and at that instant its deceleration is 0.12 ms2. The car passes R at time t = 18 with velocity 2.96 ms-1. %3D (b) Determine the values of a and b. (e) Find, to the nearest metre, the distance between points P and Rarrow_forwardSolve the following problems completely: 1. An athlete jogs north 5.0 km at 4.0 km/h and then west 12 km at 8.0 km/hr. Determine: a) the total distance of the entire trip b) the total displacement of the entire trip c) the average speed of the entire trip d) the average velocity of the entire trip e) the average acceleration of the entire trip 2. A swimmer heads directly across a river swimming at 1.8 m/s relative to still water. She arrives at a point 65 m downstream from the point directly across the river, which is 50 m wide. Determine: a) the speed of the current b) the magnitude of the swimmer's resultant velocity c) the direction of the swimmer's resultant velocity d) the time it takes the swimmer to cross the riverarrow_forward0, y 0) 44. A projectile is launched from the point (x QC with velocity (12.0î + 49.0 j) m/s, at t = 0. (a) Make a table listing the projectile's distance |r| from the ori- gin at the end of each second thereafter, for 0 s I S 10 s. Tabulating the x and y coordinates and the compo- nents of velocity v and v will also be useful. (b) Notice that the projectile's distance from its starting point increases with time, goes through a maximum, and starts to decrease. Prove that the distance is a maximum when the position vector is perpendicular to the veloc- ity. Suggestion: Argue that if v is not perpendicular to f, then r|must be increasing or decreasing. (c) Determine the magnitude of the maximum displacement. (d) Explainarrow_forward
- A boy travels from A to B and then from B to C in a bicycle. The total displacement is 3m (a) 7m (b) 0 m (c) 5 m (d) 1 m 90° 4m 3.arrow_forwardThe position of a particle that moves along the x-axis is given by x = t 3 – 3t 2 – 45t m | where tis the time in seconds. Determine the position, velocity, acceleration, and distance traveled at t= 8 s.arrow_forwardv → = ( 6 t − 4 t 2 ) i ^ − 8 j ^. Here v → is in meters per second and t in seconds. (a) What are the position, speed, and acceleration of the particle when t = 4.3 s? (b) When (if ever) is the acceleration zero? Prove your answer. (c) When (if ever) is the velocity zero? Prove your answer.arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningGlencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-Hill