A jet plane is cruising at 300 m/s when suddenly the pilot turns the engines up to full throttle. After traveling 4.0 km, the jet is moving with a speed of 400 m/s. What is the magnitude of the jet's acceleration, assuming it to be a constant acceleration?

When you sneeze, the air in your lungs accelerates from rest to 150 km/h in approximately 0.50 s. What is the magnitude of the acceleration of the air in m/s²?

A speed skater moving to the left across frictionless ice at 8.0 m/s hits a 5.0-m-wide patch of rough ice. She slows steadily, then continues on at 6.0 m/s. What is her acceleration on the rough ice?

A Porsche challenges a Honda to a 400 m race. Because the Porsche's acceleration of 3.5 m/s² is larger than the Honda's 3.0 m/s², the Honda gets a 1.0 s head start. Who wins? By how many seconds?

FIGURE EX1.18 shows the motion diagram of a drag racer. The camera took one frame every 2 s. Make a position-versus-time graph for the drag racer. Because you have data only at certain instants, your graph should consist of dots that are not connected together.

Write a short description of the motion of a real object for which FIGURE EX1.20 would be a realistic position-versus-time graph.

Ball bearings are made by letting spherical drops of molten metal fall inside a tall tower—called a shot tower—and solidify as they fall. If a bearing needs 4.0 s to solidify enough for impact, how high must the tower be?

Ball bearings are made by letting spherical drops of molten metal fall inside a tall tower—called a shot tower—and solidify as they fall. What is the bearing's impact velocity?

A rock is tossed straight up from ground level with a speed of 20 m/s. When it returns, it falls into a hole 10 m deep. What is the rock's speed as it hits the bottom of the hole?

As a science project, you drop a watermelon off the top of the Empire State Building, 320 m above the sidewalk. It so happens that Superman flies by at the instant you release the watermelon. Superman is headed straight down with a speed of 35 m/s. How fast is the watermelon going when it passes Superman?

When jumping, a flea accelerates at an astounding 1000 m/s², but over only the very short distance of 0.50 mm. If a flea jumps straight up, and if air resistance is neglected (a rather poor approximation in this situation), how high does the flea go?

A car traveling at 30 m/s runs out of gas while traveling up a 10° slope. How far up the hill will it coast before starting to roll back down?

A skier is gliding along at 3.0 m/s on horizontal, frictionless snow. He suddenly starts down a 10° incline. His speed at the bottom is 15 m/s. What is the length of the incline?

A bicycle coasting at 8.0 m/s comes to a 5.0-m-long, 1.0-m-high ramp. What is the bicycle's speed as it leaves the top of the ramp?

A snowboarder glides down a 50-m-long, 15° hill. She then glides horizontally for 10 m before reaching a 25° upward slope. Assume the snow is frictionless. How far can she travel up the 25° slope?

FIGURE EX2.31 shows the acceleration-versus-time graph of a particle moving along the x-axis. Its initial velocity is v_0x = 8.0 m/s at t₀ = 0 s. What is the particle’s velocity at t = 4.0s?

FIGURE EX2.32 shows the acceleration graph for a particle that starts from rest at t = 0 s. What is the particle's velocity at t = 6 s?

A particle moving along the x-axis has its position described by the function x = (2t³ + 2t + 1) m, where t is in s. At t = 2s, what are the particle's position?

A particle moving along the x-axis has its veocity described by the function v_x = 2t² m/s, where t is in s. itsinitial position is x₀ = 1 m at t₀ = 0 s. At t = 1 s, what are the particle's position?

The vertical position of a particle is given by the function y = (t² - 4t + 2) m, where t is in s. What is the particle's position at that time?

The position of a particle is given by the function x = (2t³ = 6t² + 12) m, where t is in s. At what time does the particle reach its minimum velocity? What is (v_x)_min?

The position of a particle is given by the function x = (2t³ - 6t² + 12) m, where t is in s. At what time is the acceleration zero?

A block is suspended from a spring, pulled down, and released. The block's position-versus-time graph is shown in FIGURE P2.38. At what times is the velocity zero? At what times is the velocity most positive? Most negative?

A block is suspended from a spring, pulled down, and released. The block's position-versus-time graph is shown in FIGURE P2.38. Draw a reasonable velocity-versus-time graph.

A particle's velocity is described by the function vₓ = (t² - 7t + 10) m/s, where t is in s. What is the particle's acceleration at each of the turning points?

A particle's velocity is described by the function vₓ =kt² m/s, where k is a constant and t is in s. The particle's position at t₀ = 0 s is x₀ = -9.0 m. At t₁ = 3.0 s, the particle is at x₁ = 9.0 m. Determine the value of the constant k. Be sure to include the proper units.

A particle's velocity is given by the function $v_x=\left(2.0\text{m/s}\right)\sin \left(\pi t\right)$, where $t$ is in $s$. What is the first time after $t=0\text{ s}$ when the particle reaches a turning point?

A particle's velocity is given by the function $\mathcal{v}_x = (2.0 \, \text{m/s}) \sin(\pi t)$, where $t$ is in $s$. What is the particle's acceleration at that time?

Draw position, velocity, and acceleration graphs for the ball shown in FIGURE P2.44. See Problem 43 for more information.

FIGURE P2.45 shows a set of kinematic graphs for a ball rolling on a track. All segments of the track are straight lines, but some may be tilted. Draw a picture of the track and also indicate the ball's initial condition.