Kinematics: Test Review

Key facts

Where marks get lost

• ×Reporting a vector as a bare number. $6.0\text{m}$ is not a displacement; $6.0\text{m}[\text{W}]$ is. (Describing Motion: Scalars, Vectors and Measurement)
• ×Using total distance where the question said displacement. The two differ exactly when the object reverses direction, which is precisely when examiners ask. (Describing Motion: Scalars, Vectors and Measurement)
• ×Writing $\Delta d=d_i-d_f$. Delta is always final minus initial — backwards flips the sign of every answer that follows. (Describing Motion: Scalars, Vectors and Measurement)
• ×Substituting km/h into a formula that returns metres and seconds. Convert first: divide by $3.6$. (Describing Motion: Scalars, Vectors and Measurement)
• ×Copying the whole calculator display. $26.5957\dots$ claims six-figure precision from a stopwatch that gave two. (Describing Motion: Scalars, Vectors and Measurement)
• ×Switching the positive direction partway through, so the two legs of a trip are measured against different conventions. (Describing Motion: Scalars, Vectors and Measurement)
• ×Reading a $d$-$t$ graph as a picture of the journey, so a rising then falling line is described as going over a hill instead of moving out and coming back. (Uniform Motion and Motion Graphs)
• ×Taking the value on a $d$-$t$ graph as the velocity. The value is a position; the slope is the velocity. (Uniform Motion and Motion Graphs)
• ×Forgetting that area below the time axis on a $v$-$t$ graph is negative displacement, so a there-and-back trip comes out with far too large a displacement. (Uniform Motion and Motion Graphs)
• ×Calculating a slope from two points that are almost on top of each other, which turns a small reading error into a large slope error. (Uniform Motion and Motion Graphs)
• ×Leaving time in minutes or hours when the velocity is in m/s. Convert before substituting, every time. (Uniform Motion and Motion Graphs)
• ×Adding magnitudes to get displacement, or adding signed values to get distance — they are computed differently and questions often ask for both. (Uniform Motion and Motion Graphs)
• ×Reading a negative acceleration as 'slowing down'. Compare it with the sign of the velocity — same signs speed up, opposite signs slow down. (Acceleration and the Kinematic Equations)
• ×Squaring only the number and not the unit, so $\frac{1}{2}a\Delta t^2$ comes out with the wrong power of seconds and the error goes unnoticed. (Acceleration and the Kinematic Equations)
• ×Using a kinematic equation across an interval where the acceleration changed. They are valid only for uniform acceleration — split the journey up. (Acceleration and the Kinematic Equations)
• ×Substituting numbers before rearranging, then trying to unpick a squared term buried inside an expression. (Acceleration and the Kinematic Equations)
• ×Forgetting that ${\vec{v}}_f=0$ for anything that comes to rest, and then claiming there is not enough information. (Acceleration and the Kinematic Equations)
• ×Taking the positive root of a quadratic for $\Delta t$ without checking, or keeping a negative time as a valid answer. (Acceleration and the Kinematic Equations)
• ×Saying the acceleration is zero at the top of a throw. The velocity is zero there; the acceleration is still $9.81{\text{m/s}}^2$ downward. (Free Fall and Motion in Two Dimensions)
• ×Mixing sign conventions inside one problem — an upward initial velocity entered as positive alongside a downward $g$ also entered as positive. (Free Fall and Motion in Two Dimensions)
• ×Setting the displacement to twice the maximum height for a ball that returns to the thrower. It comes back to where it started, so $\Delta \vec{d}=0$. (Free Fall and Motion in Two Dimensions)
• ×Writing $[\text{E }53^{\circ }\text{ N}]$ when the working measured the angle from north. The first letter names the axis you started from. (Free Fall and Motion in Two Dimensions)
• ×Adding perpendicular vectors arithmetically: $45+60=105$ is a distance travelled, not a displacement. (Free Fall and Motion in Two Dimensions)
• ×Letting a river current change the crossing time. A perpendicular current sweeps the boat downstream without affecting how fast it crosses. (Free Fall and Motion in Two Dimensions)
• ×Leaving the calculator in radian mode, so every ${\tan }^{-1}$ comes back as a small decimal instead of a sensible angle in degrees. (Free Fall and Motion in Two Dimensions)
• ×Plotting an interval velocity at the end of its interval instead of at the midpoint, which shifts the whole velocity-time line sideways and biases the intercept. (Analysing Motion Data from an Experiment)
• ×Joining the plotted points dot-to-dot. A line of best fit is one straight line through the scatter; a zig-zag has no slope worth taking. (Analysing Motion Data from an Experiment)
• ×Taking the slope from two plotted data points rather than from two points on the drawn line — the line is the averaged result, the individual points are not. (Analysing Motion Data from an Experiment)
• ×Reporting a slope as a bare number. Divide the units as well: metres per second divided by seconds is ${\text{m/s}}^2$, which is what identifies the slope as an acceleration. (Analysing Motion Data from an Experiment)
• ×Calling a consistently low result a random error. Random errors scatter both ways; an error that always pushes the same direction is systematic and averaging will never remove it. (Analysing Motion Data from an Experiment)

Practice test

25 questions from across the unit. Each one shows the lesson it comes from.

Endless drill

Fresh numbers every time, for the calculation questions in this unit.