2. 1D Motion / Kinematics

For an object starting from rest and accelerating with constant acceleration, distance traveled is proportional to the square of the time. If an object travels 2.0 furlongs in the first 2.0 s, how far will it travel in the first 4.0 s?

A robot used in a pharmacy picks up a medicine bottle at t = 0. It accelerates at 0.20 m/s² for 4.5 s, then travels without acceleration for 68 s and finally decelerates at ―0.40 m/s² for 2.5 s to reach the counter where the pharmacist will take the medicine from the robot. From how far away did the robot fetch the medicine?

A ball starts from rest and accelerates uniformly at $a$ for a time $t$. Which equation gives the distance $s$ it travels in that time?

An object moves with a constant velocity of $2m/s$. During which time interval does the object travel approximately $10m$?

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.)

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.

Find an expression for the minimum stopping distance d_stop of a car traveling at speed v₀ if the driver's reaction time is T_react and the magnitude of the acceleration during maximum braking is a constant a_brake.

A sprinter can accelerate with constant acceleration for 4.0 s before reaching top speed. He can run the 100 meter dash in 10.0 s. What is his speed as he crosses the finish line?

A car slows down from 28 m/s to rest in 6.3 s. What was its (constant) acceleration?

You throw a 5.5 g coin straight down at 4.0 m/s from a 35-m-high bridge. What is the speed of the coin just as it hits the water?

What constant acceleration, in SI units, must a car have to go from zero to 60 mph in 10 s?

Show that $\bar{v}=(v+v_0)/2$ (see Eq. 2–12d) is not valid when the acceleration $a=A+Bt$, where A and B are non-zero constants.

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.)

A speed skater moving to the left across frictionless ice at 8.0 m/s hits a 5.0-m-wide patch of rough ice. She slows steadily, then continues on at 6.0 m/s. What is her acceleration on the rough ice?