Unit 1 check

Unit 1 check: Kinematics

10 questions from 5 lessons in Unit 1. Answer each one, and if you miss, follow the link back to where it is taught, then try again. Your score counts first tries.

Question 1 · from 1.1 · Decide and justify

A runner on a circular track holds a steady 6 m/s for a full lap. Her coach says that because her speed never changes, her velocity never changes either. Is the coach right?

Which reason supports your answer?

Question 2 · from 1.2 · Calculate

A tennis ball flies toward a wall at 30 m/s and bounces straight back at 20 m/s. It touches the wall for 0.010 s. Take the direction toward the wall as positive. What is the ball's average acceleration while it touches the wall?

Your answer m/s²

Setup for question 3

On paper. For the cart in the sketch question, draw its position graph for the same 4 s directly above your velocity sketch, on the same time scale, with the cart starting at the origin. Use the velocity graph to decide where the position graph is steepest and whether it is ever level. Then draw the cart's motion diagram with a dot every second, and check that its gaps tell the same story as your two graphs.

Question 3 · from 1.3 · Sketch the graph

A cart starts from rest on a level track; take forward as positive. Its acceleration is $a_{x} = 6 - 3 t$ , with $a_{x}$ in m/s² and $t$ in seconds. Sketch its velocity against time from 0 to 4 s. The first point is fixed at 0.

Drag a point up or down, or tap it and use the arrow keys. The shape is checked, and so are the values the question lets you work out.

Question 4 · from 1.4 · Decide and justify

A train moves east along a straight track at a constant 15 m/s relative to the ground. A passenger holds a coin still and lets it go. A person on the platform watches the same coin fall. Is the coin's acceleration measured by the person on the platform the same as the acceleration measured by the passenger?

Which reason supports your answer?

Setup for question 5

On paper. For the kicked ball in Watch it done, sketch its path with $x$ and $y$ axes labeled in meters. Mark its positions at $t = 0$ , 1.5 s and 3.0 s. At each one, draw the velocity as an arrow, then draw its horizontal and vertical component arrows from the same point, labeled with their values. Use the same length for every 5 m/s. There is nothing to submit; check that your horizontal arrows are all the same length and that your vertical arrows shrink, vanish at the top and grow again pointing down.

Question 5 · from 1.5 · Rank it

Three balls are launched from the same spot on level ground, with $+ x$ horizontal and $+ y$ up; ignore air resistance. Their launch velocities, in m/s, are: ball A, $(10 \hat{i} + 10 \hat{j})$ ; ball B, $(20 \hat{i} + 10 \hat{j})$ ; ball C, $(5 \hat{i} + 15 \hat{j})$ . Rank the balls by how long each stays in the air.

Longest first

Give each one a place, 1 for first. Give two the same place if they are equal.

Ball A
Ball B
Ball C

Your ranking: none yet

Question 6 · from 1.1 · Fill the statement

A cart rolls along a straight track at 4 m/s toward the west. Take east as positive, and draw velocity arrows at a scale of 1 cm for every 2 m/s.

The cart's speed is , its velocity is $v_{x} =$ , and its velocity arrow is long.

Question 7 · from 1.2 · Decide and justify

A cart moves along a track with its position given by $x (t) = 5 t^{2} - t^{3}$ , with $x$ in meters and $t$ in seconds. Take the direction of increasing $x$ as positive. At $t = 2$ s, is the cart speeding up or slowing down?

Which reason supports your answer?

Setup for question 8

Question 8 · from 1.3 · Calculate

Two identical cars brake on the same dry road with the same constant acceleration until they stop. Car B is moving 3 times as fast as car A when its brakes go on. What is the ratio of B's stopping distance to A's, $d_{B} / d_{A}$ ?

Your answer

Setup for question 9

On paper. Draw kayaker C's velocities to scale, tip to tail, with a labeled scale such as 1 cm for 0.5 m/s: her velocity relative to the water, then the current's velocity relative to the shore from its tip, then their sum from the start of the first to the tip of the second. Label each arrow with what it is relative to. Measure the angle between her heading and her actual path, and check it against $\tan^{- 1} (\frac{1.5}{2.0}) \approx 37 °$ .

Question 9 · from 1.4 · Rank it

A wide river flows east at 1.5 m/s relative to the shore. Three kayakers each paddle at 2.0 m/s relative to the water: kayaker A points east, downstream; kayaker B points west, upstream; and kayaker C points north, straight across. Rank the kayakers by their speed relative to the shore.

Fastest first

Give each one a place, 1 for first. Give two the same place if they are equal.

Kayaker A
Kayaker B
Kayaker C

Your ranking: none yet

Setup for question 10

Question 10 · from 1.5 · Calculate

A rover starts at the origin of a flat test field, with east as $+ x$ and north as $+ y$ . At $t = 0$ its velocity is $3.0 \hat{j}$ m/s, and its acceleration is $\vec{a} (t) = 6 t \hat{i}$ , with $a$ in m/s² and $t$ in seconds. How far is the rover from its starting point at $t = 2.0$ s?

Your answer m

0 of 10 answered.