Word Problems - Kinematics | Show Me The Physics

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Review - drag and drop the runners on the track to show constant velocity and acceleration

Fill In The Blanks Notes

Review

Drag and drop the runners on the track below to show:
a) constant velocity b) acceleration

Drag and Drop Displacement

Video Instruction

showmethephysics.com

Problem-Solving Strategy

E. Solving Problems Using the Motion Equations

Ex 3

Given

Starting from rest, an object accelerates at a rate of 12 m/s².
Find: the velocity of the object at the end of 3.0 seconds.

↓

V_i = 0 a = 12 m/s² t = 3.0 sec

a = (V_f − V_i)/t →
12 m/s² = (V_f − 0)/3.0 sec

V_f = 36 m/s

Motion map showing velocity at each second

Motion Map — 1st sec / 2nd sec / 3rd sec: 12 m/s / 24 m/s / 36 m/s

Ex 4

Tip: underline the given information in the problem.

Given

An object at 100. m/s accelerates at a rate of 120. m/s².
Find: the velocity of this object after .100 seconds.

↓

a = (V_f − V_i)/t →
120. m/s² = (V_f − 100. m/s)/.100 s

Cross Multiply: 12.0 = (V_f − 100.)

V_f = 112 m/s

3 Ways to Have Non-Zero Acceleration

(to change velocity)

F. Motion Terms and Direction

A whole branch of mathematics is required to deal with numbers that have direction: Trigonometry. This is why it is important to know which motion information has direction.

Vector

A quantity that includes magnitude (a number) & direction.

ex) displacement, acceleration, velocity

Scalar

A quantity that includes magnitude (a number) only.

ex) time, distance, speed

Enrichment: Invisible Flame

Relight a Candle from Afar

Video

Show Me The Physics YouTube Channel

Check Your Understanding

5 quick questions — pick an answer to see if you’re right.

1. Starting from rest, an object accelerates at 4.0 m/s² for 3.0 s. What is its final velocity?

2. An object moving at 50. m/s accelerates at 20. m/s² for 0.50 s. What is its final velocity?

3. Which quantity is a vector?

4. Which quantity is a scalar?

5. Which object is NOT accelerating?

NYSSLS Regents Practice · Kinematics · Engineering Design

How Long Must a Runway Be?

Airport engineers are designing a runway for a small jet. Starting from rest, the jet accelerates uniformly at 3.0 m/s² and must reach a takeoff speed of 72 m/s. If a problem occurs, the pilot can abort the takeoff and brake at 5.0 m/s².

What is the minimum distance the jet needs to reach takeoff speed?

▶ Want a challenge? Open 6 more Regents-style questions (harder · mixed formats)

Challenge score: 0 / 6

Multiple choice

C1. While the jet is braking on the runway (moving forward), which row correctly describes the directions of its velocity and acceleration?

Substitute values

C2. Substitute numerical values into a mathematical representation that can be used to determine the time the jet needs to reach takeoff speed from rest. Then calculate the time.

t = m/s m/s² = s

Support or Refute · Justify

C3. A student makes the following claim.

Claim: A jet with twice the takeoff speed (144 m/s) and the same acceleration would need a runway only twice as long.

Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.

Support Refute

Multiple choice

C4. Safety rules require that a jet can reach takeoff speed and then abort and stop on the runway. Is a 1500-m runway long enough?

Determine the value

C5. A fully loaded version of the jet can accelerate at only 2.4 m/s². Determine the minimum distance it needs to reach the same 72 m/s takeoff speed from rest.

d = m

Constructed response

C6. On a wet runway, the jet can brake at only 2.5 m/s². Using a mathematical relationship, explain whether the 1500-m runway still meets the safety rule (reach 72 m/s, then abort and stop), and propose one design solution.

Motion Plots II →