A box slides across a frictionless horizontal surface with constant acceleration 3.60 m/s and over a time interval reaches a final velocity of 13.4 m/s. (a) If its initial velocity is 6.70 m/s, what is its displacement (in m) during the time interval? (Indicate the direction with the sign of your answer.) (b) What is the distance it travels (in m) during this interval? m (c) If its initial velocity is -6.70 m/s, what is its displacement (in m) during the time interval? (Indicate the direction with the sign of your answer.) m (d) What is the total distance it travels (in m) during the interval in part (c)?

If the car in the preceding example continues to accelerate at the same rate for an additional 3.0 s, what will be the magnitude of its velocity in m/s at the end of this time?

The position of a particle moving along the x -axis varies with time according to x(t)=5.0t24.0t3 . Find (a) the velocity and acceleration of the particle as functions of time, (b) the velocity and acceleration at t=2.0s , (c) the time at which the position is a maximum, (d) the time at which the velocity Is zero, and (e) the maximum position.

In a 100-rn race, the winner is timed at 11.2 s. The second-place finisher’s time Is 11.6 s. How far Is the second-place finisher behind the winner when she crosses the finish line? Assume the velocity of each runner is constant throughout the race.

A man on a motorcycle traveling at a uniform speed of 10 m/s throws an empty can straight upward relative to himself with an initial speed of 3.0 m/s. Find the equation of the trajectory as seen by a police officer on the side of the road. Assume the initial position of the can is the point where it is thrown. Ignore air resistance.

A student at the top of a building of height h throws one ball upward with a speed of i and then throws a second ball downward with the same initial speed i. Just before it reaches the ground, is the final speed of the ball thrown upward (a) larger, (b) smaller, or (c) the same in magnitude, compared with the final speed of the ball thrown downward?

A woodpecker’s brain is specially protected from large accelerations by tendon-like attachments inside the skull. While pecking on a tree, the woodpecker’s head comes to a stop from an initial velocity of 0.600 m/s in a distance of only 2.00 mm. (a) Find the acceleration in meters per second squared and in multiples of g , where g=9.80m/s2 . (b) Calculate the stopping time. (c) The tendons cradling the brain stretch, making its stopping distance 4.50 mm (greater then the head and, hence, less acceleration of the brain). What is the brain’s acceleration, expressed in multiples of g ?

How many times higher could an astronaut jump on the Moon than on Earth if her takeoff speed is the same in both locations (gravitational acceleration on the Moon is about on-sixth of that on Earth)?

An object moves with constant acceleration 4.00 m/s2 and over a lime interval reaches a final velocity of 12.0 m/s. (a) If its initial velocity is 6.00 m/s, what is its displacement during the time interval? (b) What is the distance it travels during this interval? (c) If its initial velocity is -6.00 m/s, what is its displacement during 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.

An aging coyote cannot run fast enough to catch a roadrunner. He purchases on eBay a set of jet-powered roller skates, which provide a constant horizontal acceleration of 15.0 m/s2 (Fig. P3.57). The coyote starts at rest 70.0 m from the edge of a cliff at the instant the roadrunner zips past in the direction of the cliff. (a) Determine the minimum constant speed the roadrunner must have to reach the cliff before the coyote. At the edge of the cliff, the roadrunner escapes by making a sudden turn, while the coyote continues straight ahead. The coyotes skates remain horizontal and continue to operate while he is in flight, so his acceleration while in the air is (15.0i9.80j) m/s2. (b) The cliff is 100 m above the flat floor of the desert. Determine how far from the base of the vertical cliff the coyote lands. (c) Determine the components of the coyotes impact velocity.