Unit 1: Kinematics

A hiker walks two straight legs with displacements d₁ = (4.0 î + 3.0 ĵ) m and d₂ = (−6.0 î + 5.0 ĵ) m, drawn from a common origin in the figure. What is the magnitude of the hiker's total displacement?

A runner moves at constant speed around a circular track of radius R and completes three quarters of a lap in time T. What is the magnitude of the runner's average velocity over that time?

A particle moves along the x-axis with position x(t) = t³ − 6.0t² + 9.0t + 2.0, with x in meters and t in seconds. What total distance does it travel from t = 0 to t = 4.0 s?

A cart starts from rest at x = 0 and moves with x(t) = kt³, where k is a positive constant. How does its instantaneous velocity at time T compare with its average velocity from t = 0 to t = T?

A motorboat cuts its engine and coasts, and its velocity is $v(t)$ $= v_0e^{-t/\tau}$, where v₀ and τ are positive constants. Which expression gives the boat's acceleration in terms of its velocity v at any instant?

A probe starts at x = 0 with velocity v₀ at t = 0. Its acceleration is a(t) = bt, where b is a positive constant. What is its position x(t)?

A cart moving along the x-axis has velocity −3.0 m/s at t = 0. Its acceleration is shown in the graph. What is its velocity at t = 5.0 s?

The graph shows the position of an object moving along the x-axis. During which interval is the object's speed greatest, and why?

The graph shows the velocity of a cart moving along the x-axis. What is the cart's displacement from t = 0 to t = 5.0 s?

A ball is thrown straight up at 14 m/s from the edge of a roof 20 m above the ground and falls past the roof to the ground. How long after the throw does it reach the ground?

A robot starts from rest and its acceleration grows with time as a = ct², where c is a constant. By what factor does the distance it covers increase if it runs for 2T instead of T?

A bead slides along a wire on the x-axis. Wherever it is, its velocity is v = βx², where β is a positive constant. What is its acceleration in terms of x?

The graph shows the velocity of a cart that starts at x = 0 and moves along the x-axis. Which claim about the cart's motion is correct?

A particle's velocity is v(t) = 6.0t² − 2.0t, with v in m/s and t in seconds. At t = 0 it is at x = 3.0 m. Where is it at t = 2.0 s?

A boat crosses the 60 m wide river shown. It points straight across and moves at 4.0 m/s relative to the water, while the water flows downstream at 3.0 m/s relative to the banks. How far downstream of its starting point does the boat land?

A stone is dropped from rest from a bridge. A car passes under the bridge at a constant 20 m/s along a straight, level road. What acceleration of the stone does the driver measure while the stone falls?

Car A drives east at 15 m/s and car B drives north at 20 m/s on flat ground. What is the velocity of car B as measured by the driver of car A?

A ball rolls off a horizontal table top at speed v₀ and lands on the floor a height h below. What is its speed just before it lands?

A drone's position is r(t) = At² î + Bt ĵ, where A and B are positive constants. What is its speed at time t?

A puck starts at the origin and moves on a horizontal table with velocity v(t) = (4.0 î + 3.0t ĵ) m/s. Which describes its path?

A projectile launched from level ground at 30° above the horizontal reaches a maximum height H and lands a distance D away. It is launched again with the same speed at 60°. Which describes the new maximum height and range?

The table gives the position of a ball thrown on level ground, measured every 0.20 s. Which claim do the data support?