A car of mass $m$ accelerates from rest along a level straight track, not at a constant acceleration but with constant engine power, $P$. Assume that air resistance is negligible. c) You are in a drag race, on a straight level track, with an opponent whose car maintains a constant acceleration of $12.0 \mathrm{~m} / \mathrm{s}^2$. Both cars have identical masses of 1000 . kg. The cars start together from rest. Air resistance is assumed to be negligible. Calculate the minimum power your engine needs for you to win the race, assuming the power output is constant and the distance to the finish line is $0.250 \mathrm{mi}$.

A certain heat engine operating on a Carnot cycle absorbs 410 J of heat per cycle at its hot reservoir at $135^{\circ} C$ and has a thermal efficiency of 22.0%. (a) How much work does this engine do per cycle? (b) How much heat does the engine waste each cycle? (c) What is the temperature of the cold reservoir? (d) By how much does the engine change the entropy of the world each cycle? (e) What mass of water could this engine pump per cycle from a well 35.0 m deep?

An aircraft engine takes in $9000 \mathrm{~J}$ of heat and discards $6400 \mathrm{~J}$ each cycle.
(b) What is the thermal efficiency of the engine?

A merry-go-round has a radius of 2.0 m and a moment of inertia 300 kg·m². A boy of mass 50 kg runs tangent to the rim at a speed of 4.0 m/s and jumps on. If the merry-go-round is initially at rest, what is the angular velocity after the boy jumps on?

Three $70-\mathrm{kg}$ deer are standing on a flat $200-\mathrm{kg}$ rock that is on an ice-covered pond. A gunshot goes off and the dear scatter, with deer A running at $(15 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{i}}+(5.0 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{j}}$, deer B running at $(-12 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{i}}+(8.0 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{j}}$, and deer C running at $(1.2 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{i}}-(18.0 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{j}}$. What is the velocity of the rock on which they were standing?

Two cars approach an extremely icy four-way perpendicular intersection. Car A travels northward at 30 m/s and car B is travelling eastward. They collide and stick together, traveling at 28° north of east. What was the initial velocity of car B?

Find the exact area of the surface obtained by rotating the given curve about the x-axis. x=t^3, y=t^2, 0<=t<=1

Find the area enclosed by the curve x = t2 - 2t, y = √t and the y-axis.

A car of mass $m$ accelerates from rest along a level straight track, not at a constant acceleration but with constant engine power, $P$. Assume that air resistance is negligible. b) A second car starts from rest alongside the first car on the same track, but maintains a constant acceleration. Which car takes the initial lead? Does the other car overtake it? If yes, write a formula for the distance from the starting point at which this happens.

A car of mass $m$ accelerates from rest along a level straight track, not at a constant acceleration but with constant engine power, $P$. Assume that air resistance is negligible. a) Find the car's velocity as a function of time.

A small blimp is used for advertising purposes at a football game. It has a mass of $93.5 \mathrm{~kg}$ and is attached by a towrope to a truck on the ground. The towrope makes an angle of $53.3^{\circ}$ downward from the horizontal, and the blimp hovers at a constant height of $19.5 \mathrm{~m}$ above the ground. The truck moves on a straight line for $840.5 \mathrm{~m}$ on the level surface of the stadium parking lot at a constant velocity of $8.90 \mathrm{~m} / \mathrm{s}$. If the drag coefficient $(K$ in $F=K v^2$ ) is $0.500 \mathrm{~kg} / \mathrm{m}$, how much work is done by the truck in pulling the blimp (assuming there is no wind)?

A car of mass $942.4 \mathrm{~kg}$ accelerates from rest with a constant power output of $140.5 \mathrm{hp}$. Neglecting air resistance, what is the speed of the car after $4.55 \mathrm{~s}$ ?

The volume of two similar figures are 2 yd$^3$ and 250 yd$^3$. The surface area of the smaller figure is 13 yd$^2$. Find the surface area of the larger figure.

An engine expends $40.0 \mathrm{hp}$ in moving a car along a level track at a speed of $15.0 \mathrm{~m} / \mathrm{s}$. How large is the total force acting on the car in the direction opposite to the motion of the car?