A car starts from rest and accelerates at a variable rate given by the equation a(t) = 2t + 3 m/s², where t is the time in seconds. Estimate the change in velocity of the car from t=0 s to t=4 s using the trapezoidal rule with two intervals.

A barge is being towed at 16 m/s when the towline breaks. It continues thereafter in a straight line but slows down at a rate proportional to the square root of its instantaneous velocity. If two minutes after the tow line breaks, the velocity is 9 m/s, how far does it move before coming to rest?

A boxer's fist and glove have a mass of m = 1.04 kg. The boxer's fist can obtain a speed of v = 9.25 m/s in a time of t = 0.21 s. Write a symbolic expression for the magnitude of the average acceleration, aave, of the boxer's fist, in terms of the variables provided.  Find the magnitude of the average acceleration, aave, in meters per square second. Write an expression for the magnitude of the average net force, Fb, that the boxer must apply to his fist to achieve the given velocity. (Write the expression in terms of m, v and t.) What is the numerical value of Fb, in newtons?

Problem 5 2.68 A rigid ball traveling in straight line (the x-axis) hits a solid wall and suddenly rebounds during a brief instant. The vy-t graph shows this Vx (m/s) 30.0 ball's velocity as a function of time. During the first 20.0 s of its motion, find: (a) the total distance the ball moves and (b) its displacement. (c) Sketch a graph of ax-t for this ball's motion. 20.0 (d) Is the graph shown really vertical at 5.0 s? Explain. 10.0 t (s) 5.0 10,0 15.0 20,0 Total distance traveled = 225.0 m a) b) Displacement = -75.0 m %3D -10.0 -20.0

An unidentified flying object (UFO) is observed to travel a total distance of 42000 m, starting and ending at rest, over a duration of 2.07 s. Assuming the UFO accelerated at a constant rate to the midpoint of its journey and then decelerated at a constant rate the rest of the way, what was the magnitude of its acceleration? Express your answer in g s , where 1 g = 9.81 m/s^2.     39,207 g s     19,604 g s     3,997 g s     1,998 g s

A bullet shot straight up returns to its starting point in 63.7 s. embedding itself 15.5 cm deep in a wooden block. What is the average acceleration the bullet encounters in the block (in standard units)? Answer: Check

The acceleration of an object as a function of time is given by a(t) = 6.0 t² where t and a are in Sl units. If the object has a velocity 2.0 m/s at time t=0.0 s. What is the velocity of this object as a function of time?

A car, moving to the left in a straight line in the negative x-direction, travels a distance d = 32 m during time interval Δt = 18 s. What is the value of the x-component of the car's average velocity, in m/s, during the given time interval?

An object with mass m moves along the x axis. It is observed to have a velocity in the positive x direction with a magnitude of c_1t^2 where c_1 is a positive known constant and t is the time in seconds. At t=1s it's observed to be at the point x=D. When does the object reach x=2D?

You and your friend would like to experimentally determine a value for g, an object's acceleration due to gravity on Earth. Your friend sets a baseball on the edge of a desk, and you crouch down by the floor, waiting for the ball to drop. She pushes the ball off the desk and yells GO! to signal you to press START your phone's stopwatch app. When the ball hits the floor, you press STOP on the app to stop the timer, and see that the time reads t = 0.606 s. Using a tape measure with markings for cm, you measure the top of the desk to be h = 123 cm from the floor.  Part 1) Assuming the ball started with no initial vertical velocity, calculate the value of g in your experiment symbolically. Assume that g is a positive number.  Part 2) Using your previous symbolic answer and the qualities from the experiment, determine a numeric value for g.  Part 3) What is a reasonable quantitative estimate for your uncertainty in stopping the timer, sigma t? What about your error in measuring the height…