Conceptual Math

Kinematics & Motion (EIAT Style)

Recent test-takers have reported more questions about objects falling, being thrown, or moving at steady speed. This page walks you through the exact patterns you need to recognize so these feel simple on test day.

1. Core Ideas in Plain English

You do not need a physics degree for this section. Keep these ideas in mind:

Speed tells you how fast something moves (distance per unit of time).
Gravity pulls objects straight down and makes them speed up as they fall.
Horizontal (sideways) motion usually has constant speed in these problems.
Vertical (up/down) motion is what gravity changes.
Horizontal and vertical motion are independent. Sideways speed changes where an object lands, not when it hits the ground.

2. Simple Formulas You Actually Use

Distance, Speed, and Time

distance = speed × time

speed = distance ÷ time

time = distance ÷ speed

Make sure units match. For example: miles & hours, or feet & seconds.

Horizontal Distance for a Thrown Object

If an object is thrown or pushed sideways off a platform or floor:

horizontal distance = horizontal speed × time in the air

Time in the air depends on how far it has to fall. On the EIAT, this time is usually given in the question, so you can just plug it in.

You normally do not need the exact value of gravity (like 32 ft/s²) for EIAT-style questions. Focus on what the question is really asking for: distance, speed, or time.

3. How to Attack These Questions

Step 1: Decide what they’re asking for: distance, speed, or time.

Step 2: Pick the matching simple formula from above.

Step 3: Ignore extra numbers that don’t fit the pattern.

Step 4: Double-check units (minutes vs hours, feet vs miles).

4. Practice Questions (Paragraph Style)

Try these on your own first, then check the answer key at the bottom.

A train travels at a steady speed of 45 miles per hour for 2.5 hours. How far does it go?
A worker walks along a straight catwalk at 4 feet per second for 12 seconds. How many feet does the worker travel?
A tool is dropped straight down from a platform. At the same time, an identical tool is thrown horizontally from the same height. Ignoring air resistance, which tool hits the ground first?
A) The dropped tool
B) The thrown tool
C) They hit at the same time
D) It depends on how hard it was thrown
A worker slides a box off a platform so that it moves horizontally at 18 feet per second. It takes 2.5 seconds for the box to hit the ground. How far from the base of the platform does it land?
A moving walkway in a warehouse carries boxes at a constant 3 feet per second. A box rides on the walkway for 12 seconds. How far does the box travel while on the walkway?
Two identical bolts are thrown horizontally from the same height. Bolt A is thrown at 10 ft/s and Bolt B is thrown at 15 ft/s. Which statement is true?
A) Bolt A lands first and closer to the building.
B) Bolt B lands first and farther from the building.
C) They hit the ground at the same time, but Bolt B lands farther away.
D) They hit the ground at different times but land at the same distance.
A worker on a platform throws a small part horizontally at 14 ft/s. It is in the air for 2.5 seconds before it reaches the ground. How far from the base of the platform does the part land?
Which of the following is directly caused by gravity in these types of questions?
A) The sideways (horizontal) speed of the object
B) The rate at which the object falls downward
C) The distance between the worker and the building
D) The length of the platform
A service van travels at 60 miles per hour for 45 minutes on the way to a job site. How many miles does the van travel in that time?
A cart travels 24 miles in 30 minutes at a steady speed. What is its average speed in miles per hour?
Two tools are dropped from rest, one from 80 feet high and one from 50 feet high. Ignoring air resistance, which tool hits the ground first?
A) The one dropped from 80 feet
B) The one dropped from 50 feet
C) They hit at the same time
D) There is not enough information
A platform is 30 feet high. A worker pushes a small crate straight sideways off the edge at 20 ft/s. The crate is in the air for 2 seconds before it hits the ground. How far from the base of the platform does it land? (Hint: one of the numbers given is extra.)

Answer Key

112.5 miles – Distance = speed × time = 45 mph × 2.5 h = 112.5 miles.
48 feet – Distance = 4 ft/s × 12 s = 48 ft.
C) They hit at the same time. Gravity affects only vertical motion. Sideways motion doesn’t change fall time.
45 feet – Distance = 18 ft/s × 2.5 s = 45 ft.
36 feet – Distance = 3 ft/s × 12 s = 36 ft.
C) – Same height means same fall time. Higher sideways speed → lands farther away.
35 feet – Distance = 14 ft/s × 2.5 s = 35 ft.
B) – Gravity causes the downward acceleration (how fast it falls vertically).
45 miles – 45 minutes = 0.75 hours. Distance = 60 mph × 0.75 h = 45 miles.
48 mph – 30 minutes = 0.5 hours. Speed = 24 miles ÷ 0.5 h = 48 mph.
B) The one dropped from 50 feet. Less distance to fall → less time in the air.
40 feet – Horizontal distance = speed × time = 20 ft/s × 2 s = 40 ft. The 30 ft height is extra info in this problem.

Tip: On the real test, don’t overthink the physics. Identify whether they want distance, speed, or time, plug into the simple formula, and ignore numbers that don’t fit the pattern.

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