Unit 1: Kinematics

19 terms. Say what each one means, then open the card to check.

• Scalar

  A quantity described fully by a size and a unit, with no direction, such as distance, speed, mass or time.

  Example. A mass of 3 kg, a time of 20 s and a temperature of 21 degrees Celsius each need only a number and a unit; no direction applies.

• Vector

  A quantity with both a size and a direction, such as displacement, velocity, acceleration or force. Vectors add tip to tail, not just by adding sizes.

  Example. A 30 N push toward the north and a 30 N push toward the south are different vectors, even though their sizes match.

• Displacement

  The change in position, final position minus initial position. It points from the start to the finish, whatever path was taken.

  Example. A swimmer who swims two lengths of a pool and ends at the wall where she started has zero displacement.

• Distance traveled

  The total length of the path covered. It is never negative and never smaller than the size of the displacement.

  Example. A dog that runs 12 m to fetch a stick and 12 m back covers 24 m, although its displacement is zero.

• Average velocity

  Displacement divided by the elapsed time. It points in the direction of the displacement.

  Example. A train that ends 90 km north of its start after 1.5 h has an average velocity of 60 km/h north, whatever its route.

• Average speed

  Distance traveled divided by the elapsed time. It equals the size of the average velocity only for one-way motion along a straight line.

  Example. A bus that covers 40 km of winding road in 1.0 h has an average speed of 40 km/h, even if it ends only 25 km from where it began.

• Vector components

  The perpendicular parts of a vector along chosen axes. A vector of size A at angle θ above the x-axis has $A_x = A\cos\theta$ and $A_y = A\sin\theta$.

  Example. A velocity of 12 m/s at 40 degrees above the horizontal has components of about 9.2 m/s sideways and 7.7 m/s upward.

• Acceleration

  The rate of change of velocity, $a = \Delta v/\Delta t$. An object accelerates when its speed changes, its direction changes, or both.

  Example. A car rounding a curve at a steady 15 m/s is accelerating, because the direction of its velocity keeps changing.

• Slope of a position-time graph

  The velocity. A steeper line means a faster object, and a line sloping down means motion in the negative direction.

  Example. A straight line on a position-time graph that rises 30 m in 6 s shows a constant velocity of +5 m/s.

• Slope of a velocity-time graph

  The acceleration. A horizontal line means constant velocity and zero acceleration.

  Example. A velocity-time line that falls from 12 m/s to 0 in 4 s shows an acceleration of -3 m/s².

• Area under a velocity-time graph

  The displacement over that time interval. Area between the line and the time axis counts as negative when it lies below the axis.

  Example. A constant velocity of 3 m/s held for 10 s fills a rectangle of area 30 m, so the object moved 30 m.

• Constant-acceleration equations

  Three relations that hold only when the acceleration is constant: $v = v_0 + at$, $\Delta x = v_0t + \tfrac{1}{2}at^2$ and $v^2 = v_0^2 + 2a\Delta x$.

  Example. A sled that starts at 2 m/s and gains 1 m/s every second moves at 7 m/s after 5 s, by $v = v_0 + at$.

• Free fall

  Motion under gravity alone. Near Earth’s surface every freely falling object accelerates downward at about 9.8 m/s², whatever its mass and whether it is rising or falling.

  Example. A coin and a heavy wrench dropped together inside a vacuum chamber reach the floor at the same moment.

• Reference frame

  The point of view, with its own origin and axes, from which positions and velocities are measured. Different frames can report different velocities for the same object.

  Example. A passenger dozing on a plane is at rest in the plane’s frame but moving at hundreds of kilometers per hour in the ground’s frame.

• Relative velocity

  The velocity of an object measured in a given frame. Velocities add as vectors: A relative to C equals A relative to B plus B relative to C.

  Example. A sailor walking toward the stern at 1 m/s on a ship moving forward at 6 m/s moves forward at 5 m/s relative to the water.

• Projectile

  An object moving through the air under gravity alone after it is launched. With no air resistance, its path is a parabola.

  Example. A set of keys tossed across a room follows a curved path and accelerates straight downward the whole time.

• Independence of horizontal and vertical motion

  For a projectile, the horizontal velocity stays constant while the vertical velocity changes at 9.8 m/s² downward. Time is the one quantity the two directions share.

  Example. A ball fired level and a ball dropped from the same height at the same instant would land together on level ground if there were no air.

• Time of flight

  The time a projectile spends in the air. It is set by the vertical motion alone: the launch height and the vertical part of the launch velocity.

  Example. Kicking a ball with a larger upward velocity keeps it in the air longer, whatever its sideways speed.

• Range

  The horizontal distance a projectile covers: its constant horizontal velocity times its time of flight.

  Example. A ball that moves sideways at 4 m/s and stays in the air for 1.5 s lands 6 m from its launch point, measured along the ground.