(II) A car traveling at a velocity $v$ can stop in a minimum distance $d$. What would be the car's minimum stopping distance if it were traveling at a velocity of $2v$?

A large car of mass 2 m travels at speed v. A small car of mass m travels with a speed 2v. Both skid to a stop with the same coefficient of friction. (a) The small car will have (1) a longer, (2) the same, (3) a shorter stopping distance. (b) Calculate the ratio of the stopping distance of the small car to that of the large car. (Use the work-energy theorem, not Newton's laws.)

When the speed of your car is doubled, by what factor does its kinetic energy increase? $(a)$ $\sqrt{2}$. $(b)$ 2 . $(c)$ 4 . $(d)$ 8.

The hyperbolic sine is defined as

$$\sinh{x}=\frac{e^{x}-e^{-x}}{2}.$$

The first derivative is equal to $\cosh{x}$. True or False?

Evaluate the equation by completing the square.

$$x^2+7 x-3=0$$

You push very hard on a heavy desk, trying to move it. You do work on the desk:
(a) Whether or not it moves, as long as you are exerting a force.
(b) Only if it starts moving.
(c) Only if it doesn't move.
(d) Never-it does work on you.
(e) None of the above.

(a) How much work is done by the horizontal force Fp = 150 N on the 18-kg block when the force pushes the block 5.0 m up along the 32° frictionless incline? (b) How much work is done by the gravitational force on the block during this displacement? (c) How much work is done by the normal force? (d) What is the speed of the block (assume that it is zero initially) after this displacement? [Hint. Work-energy involves net work done.]

At an accident scene on a level road, investigators measure a car's skid mark to be 78 m long. It was a rainy day and the coefficient of friction was estimated to be 0.30.

Why does the car's mass not matter?

At an accident scene on a level road, investigators measure a car's skid mark to be 78 m long. It was a rainy day and the coefficient of friction was estimated to be 0.30.

Use these data to determine the speed of the car when the driver slammed on (and locked) the brakes.

At an accident scene on a level road, investigators measure a car's skid mark to be 78 m long. It was a rainy day and the coefficient of friction was estimated to be 0.30.

What is wrong with a car that skids ?

(II) An 85-g arrow is fired from a bow whose string exerts an average force of $105 \mathrm{~N}$ on the arrow over a distance of $75 \mathrm{~cm}$. What is the speed of the arrow as it leaves the bow?

Two bullets are fired at the same time with the same kinetic energy. If one bullet has twice the mass of the other, which has the greater speed, and by what factor?

$(a)$ If the kinetic energy of a particle is tripled, by what factor has its speed increased? $(b)$ If the speed of a particle is halved, by what factor does its kinetic energy change?

(III) A spring of spring constant $k$ and negligible mass is attached to a $\operatorname{mass} m$ and the other end of the spring is pulled vertically in order to lift the mass. Find an expression for the amount of work that must be done on the spring before the mass begins to leave the ground.