A pilot who accelerates at more than $4g$ begins to 'gray out' but doesn't completely lose consciousness. Assuming constant acceleration, what is the shortest time that a jet pilot starting from rest can take to reach Mach $4$ (four times the speed of sound) without graying out? (Use $331$ m/s for the speed of sound in cold air.)

A motorist is driving at 20 m/s when she sees that a traffic light 200 m ahead has just turned red. She knows that this light stays red for 15 s, and she wants to reach the light just as it turns green again. It takes her 1.0 s to step on the brakes and begin slowing. What is her speed as she reaches the light at the instant it turns green?

At launch a rocket ship weighs $4.5$ million pounds. When it is launched from rest, it takes $8.00$ s to reach $161$ km/h; at the end of the first $1.00$ min, its speed is $1610$ km/h. What is the average acceleration (in m/s²) of the rocket (i) during the first $8.00$ s and (ii) between $8.00$ s and the end of the first $1.00$ min?

An astronaut has left the International Space Station to test a new space scooter. Her partner measures the following velocity changes, each taking place in a $10$-s interval. What are the magnitude, the algebraic sign, and the direction of the average acceleration in each interval? Assume that the positive direction is to the right.

(a) At the beginning of the interval, the astronaut is moving toward the right along the $x$-axis at $15.0$ m/s, and at the end of the interval she is moving toward the right at $5.0$ m/s.

(b) At the beginning she is moving toward the left at $5.0$ m/s, and at the end she is moving toward the left at $15.0$ m/s.

(c) At the beginning she is moving toward the right at $15.0$ m/s, and at the end she is moving toward the left at $15.0$ m/s.

A pilot who accelerates at more than $4g$ begins to 'gray out' but doesn't completely lose consciousness. How far would the plane travel during this period of acceleration? (Use $331$ m/s for the speed of sound in cold air.)

In the fastest measured tennis serve, the ball left the racquet at $73.14$ m/s. A served tennis ball is typically in contact with the racquet for $30.0$ ms and starts from rest. Assume constant acceleration. What was the ball's acceleration during this serve?

The fastest measured pitched baseball left the pitcher's hand at a speed of $45.0$ m/s. If the pitcher was in contact with the ball over a distance of $1.50$ m and produced constant acceleration, what acceleration did he give the ball?

An antelope moving with constant acceleration covers the distance between two points $70.0$ m apart in $6.00$ s. Its speed as it passes the second point is $15.0$ m/s. What is its acceleration?

The human body can survive an acceleration trauma incident (sudden stop) if the magnitude of the acceleration is less than $250$ m/s². If you are in an automobile accident with an initial speed of $105$ km/h ($65$ mi/h) and are stopped by an airbag that inflates from the dashboard, over what distance must the airbag stop you for you to survive the crash?