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 freight truck collides head-on with a passenger car, causing a lot more damage to the car than to the truck. From this condition, we can say that (a) the magnitude of the force of the truck on the car is greater than the magnitude of the force of the car on the truck, (b) the magnitude of the force of the truck on the car is smaller than the magnitude of the force of the car on the truck, (c) the magnitude of the force of the truck on the car is equal to the magnitude of the force of the car on the truck, (d) none of the preceding.

A light plane must reach a speed of $30$ m/s for takeoff. How long a runway is needed if the (constant) acceleration is $3.0$ m/s$^2?$

Suppose you follow these directions. Face north. Walk four feet. Turn right. Walk six feet. Turn right again. Walk for feet. Turn right again and walk six feet. Turn right again. a. What shape will your path form? b. In what direction will you be facing when you finish? c. The direction turn right does not specify how far to turn. Yet you probably made an assumption. What was your assumption? What makes it seem reasonable?

A 1200-kg car moving to the right with a speed of 25 m/s collides with a 1500-kg truck and locks bumpers with the truck. Calculate the velocity of the combination after the collision if the truck is initially (a) at rest, (b) moving to the right with a speed of 20 m/s, and (c) moving to the left with a speed of 20 m/s.

The position of an object as a function of time is given by x=bt^2-ct, where b=2.0 m/s^2 and c=6.7 m\s, and x and t are in SI units. What is the instantaneous velocity of the object when t=2.2?

Suppose you walk north 10 paces, turn left through $24^{\circ}$, walk 10 paces, turn left through $24^{\circ}$, walk 10 paces, and so on.
(a) Will you return to your starting point?
(b) What is the shape of the path?

James and John dive from an overhang into the lake below James simply drops straight down from the edge. John takes a running start and jumps with an initial horizontal velocity of 25 m/s. Compare the time it takes each to reach the lake below if there is no air resistance.

a) James reaches the surface of the lake first.

b) John reaches the surface of the lake first.

c) James and john will reach the surface of the lake at the same time.

d) Cannot be determined without knowing the mass of both James and John.

A ball rolls off a table with a horizontal velocity of $5 \mathrm{~m} / \mathrm{s}$. Is this velocity an important factor in determining the time that it takes for the ball to hit the floor? Explain.

A man drops a stone from a bridge. What is the height of the bridge if the sound of the splash reaches the man 4s later? [Take 1080ft/s as the speed of sound.]

The highest point of the Mike O'Callaghan-Pat Tillman Memorial Bridge is $890 \mathrm{ft}$ above the Colorado River. How long will it take a stone to fall from the bridge to the river?

An airplane starts from rest and accelerates at $12.1 \mathrm{~m} / \mathrm{s}^2$. What is its speed at the end of a 500 .-m runway?

An airplane starts from rest and accelerates at $12.1 \mathrm{~m} / \mathrm{s}^2$. What is its speed at the end of a $500 .-\mathrm{m}$ runway?

You want to nail a $1.6-\mathrm{kg}$ board onto the wall of a barn. To position the board before nailing, you push it against the wall with a horizontal force $\overrightarrow{\mathbf{F}}$ to keep it from sliding to the ground . If the coefficient of static friction between the board and the wall is $0.79$, what is the least force you can apply and still hold the board in place?