A cat walks in a straight line, which we shall call the $x$-axis, with the positive direction to the right. As an observant physicist, you make measurements of this cat's motion and construct a graph of the feline's velocity as a function of time (Fig. E$2.30$). Assuming that the cat started at the origin, sketch clear graphs of the cat's acceleration and position as functions of time.

A small block has constant acceleration as it slides down a frictionless incline. The block is released from rest at the top of the incline, and its speed after it has traveled $6.80$ m to the bottom of the incline is $3.80$ m/s. What is the speed of the block when it is $3.40$ m from the top of the incline?

At the instant the traffic light turns green, a car that has been waiting at an intersection starts ahead with a constant acceleration of $2.80$ m/s². At the same instant a truck, traveling with a constant speed of $20.0$ m/s, overtakes and passes the car. How far beyond its starting point does the car overtake the truck?

At the instant the traffic light turns green, a car that has been waiting at an intersection starts ahead with a constant acceleration of $2.80$ m/s². At the same instant a truck, traveling with a constant speed of $20.0$ m/s, overtakes and passes the car. How fast is the car traveling when it overtakes the truck?

If a flea can jump straight up to a height of $0.440$ m, what is its initial speed as it leaves the ground?

If a flea can jump straight up to a height of $0.440$ m, How long is it in the air?

A small rock is thrown vertically upward with a speed of $22.0$ m/s from the edge of the roof of a $30.0$-m-tall building. The rock doesn't hit the building on its way back down and lands on the street below. Ignore air resistance. What is the speed of the rock just before it hits the street?

A small rock is thrown vertically upward with a speed of $22.0$ m/s from the edge of the roof of a $30.0$-m-tall building. The rock doesn't hit the building on its way back down and lands on the street below. Ignore air resistance. How much time elapses from when the rock is thrown until it hits the street?

A juggler throws a bowling pin straight up with an initial speed of $8.20$ m/s. How much time elapses until the bowling pin returns to the juggler's hand?

You throw a glob of putty straight up toward the ceiling, which is $3.60$ m above the point where the putty leaves your hand. The initial speed of the putty as it leaves your hand is $9.50$ m/s. What is the speed of the putty just before it strikes the ceiling?

You throw a glob of putty straight up toward the ceiling, which is $3.60$ m above the point where the putty leaves your hand. The initial speed of the putty as it leaves your hand is $9.50$ m/s. How much time from when it leaves your hand does it take the putty to reach the ceiling?

A tennis ball on Mars, where the acceleration due to gravity is $0.379g$ and air resistance is negligible, is hit directly upward and returns to the same level $8.5$ s later. How high above its original point did the ball go?

A tennis ball on Mars, where the acceleration due to gravity is $0.379g$ and air resistance is negligible, is hit directly upward and returns to the same level $8.5$ s later. How fast was it moving just after it was hit?

A lunar lander is making its descent to Moon Base I (Fig. E$2.40$). The lander descends slowly under the retro-thrust of its descent engine. The engine is cut off when the lander is $5.0$ m above the surface and has a downward speed of $0.8$ m/s. With the engine off, the lander is in free fall. What is the speed of the lander just before it touches the surface? The acceleration due to gravity on the moon is $1.6$ m/s.

A brick is dropped (zero initial speed) from the roof of a building. The brick strikes the ground in $1.90$ s. You may ignore air resistance, so the brick is in free fall. How tall, in meters, is the building?

A brick is dropped (zero initial speed) from the roof of a building. The brick strikes the ground in $1.90$ s. You may ignore air resistance, so the brick is in free fall. What is the magnitude of the brick's velocity just before it reaches the ground?

A $7500$-kg rocket blasts off vertically from the launch pad with a constant upward acceleration of $2.25$ m/s² and feels no appreciable air resistance. When it has reached a height of $525$ m, its engines suddenly fail; the only force acting on it is now gravity. What is the maximum height this rocket will reach above the launch pad?

A $7500$-kg rocket blasts off vertically from the launch pad with a constant upward acceleration of $2.25$ m/s² and feels no appreciable air resistance. When it has reached a height of $525$ m, its engines suddenly fail; the only force acting on it is now gravity. How much time will elapse after engine failure before the rocket comes crashing down to the launch pad, and how fast will it be moving just before it crashes?

A hot-air balloonist, rising vertically with a constant velocity of magnitude $5.00$ m/s, releases a sandbag at an instant when the balloon is $40.0$ m above the ground (Fig. E$2.44$). After the sandbag is released, it is in free fall. Compute the position and velocity of the sandbag at $0.250$ s and $1.00$ s after its release.

A hot-air balloonist, rising vertically with a constant velocity of magnitude $5.00$ m/s, releases a sandbag at an instant when the balloon is $40.0$ m above the ground (Fig. E$2.44$). After the sandbag is released, it is in free fall. What is the greatest height above the ground that the sandbag reaches?

An egg is thrown nearly vertically upward from a point near the cornice of a tall building. The egg just misses the cornice on the way down and passes a point $30.0$ m below its starting point $5.00$ s after it leaves the thrower's hand. Ignore air resistance. What is the initial speed of the egg?

An egg is thrown nearly vertically upward from a point near the cornice of a tall building. The egg just misses the cornice on the way down and passes a point $30.0$ m below its starting point $5.00$ s after it leaves the thrower's hand. Ignore air resistance. How high does it rise above its starting point?

An egg is thrown nearly vertically upward from a point near the cornice of a tall building. The egg just misses the cornice on the way down and passes a point $30.0$ m below its starting point $5.00$ s after it leaves the thrower's hand. Ignore air resistance. What is the magnitude of its velocity at the highest point?

An egg is thrown nearly vertically upward from a point near the cornice of a tall building. The egg just misses the cornice on the way down and passes a point $30.0$ m below its starting point $5.00$ s after it leaves the thrower's hand. Ignore air resistance. What are the magnitude and direction of its acceleration at the highest point?

A $15$-kg rock is dropped from rest on the earth and reaches the ground in $1.75$ s. When it is dropped from the same height on Saturn's satellite Enceladus, the rock reaches the ground in $18.6$ s. What is the acceleration due to gravity on Enceladus?

A large boulder is ejected vertically upward from a volcano with an initial speed of $40.0$ m/s. Ignore air resistance. At what time after being ejected is the boulder moving at $20.0$ m/s upward?

A large boulder is ejected vertically upward from a volcano with an initial speed of $40.0$ m/s. Ignore air resistance. At what time is it moving at $20.0$ m/s downward?

A large boulder is ejected vertically upward from a volcano with an initial speed of $40.0$ m/s. Ignore air resistance. When is the displacement of the boulder from its initial position zero?

A large boulder is ejected vertically upward from a volcano with an initial speed of $40.0$ m/s. Ignore air resistance. When is the velocity of the boulder zero?

A large boulder is ejected vertically upward from a volcano with an initial speed of $40.0$ m/s. Ignore air resistance. What are the magnitude and direction of the acceleration while the boulder is (i) moving upward? (ii) Moving downward? (iii) At the highest point?