Motion Equations for Problem Solving - Kinematics

← Motion Plots Summary All Lessons Word Problems →

Motion Equations for problem solving with constant acceleration

Fill In The Blanks Notes

Warm-Up

One of these things is not like the other!

Is the Acceleration Constant, Increasing or Zero?

Review

Click on the button and play ...

View the original GIF

The idea for this game and graphic come from a great high school physics teacher named Kelly O'Shea.

Video Instruction

showmethephysics.com

IV. Motion Equations for Problem Solving

When an object is moving at a constant acceleration we can use the following equations to find motion information.

A. Constant Accel. Equations

(see Reference Table)

1. Average Velocity

V = (V_i + V_f)/2 or V = Δd/Δt

2. Acceleration

a = (V_f − V_i)/t

Cross multiply & Solve: at = (V_f − V_i)

Add V_i to both sides

V_f = V_i + at

3. Displacement

V = Δd/Δt

B. Additional Equations

Take Equation 3 and solve for d

Δd = VΔt

Substitute Equation 1 into the previous equation

Δd = [(V_i + V_f)/2]Δt

Since V_f = V_i + at

Δd = [(V_i + (V_i + at))/2]Δt

Gather like terms and solve for d

Δd = V_it + ½at²

Try This at Home!

“30 Seconds with Mr. G” - Number 4, Mindpaint Channel

Mindpaint Channel

Check Your Understanding

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

1. The constant acceleration motion equations can be used only when...

2. A car's velocity goes from 4 m/s to 10 m/s with constant acceleration. What is its average velocity?

3. An object moving at 5 m/s accelerates at 3 m/s² for 4 s. What is its final velocity?

4. Starting from rest, an object accelerates at 2 m/s² for 5 s. How far does it travel?

5. You know Vi, a, and t and want the final velocity. Which equation fits best?

NYSSLS Regents Practice · Kinematics · Mathematical Models

Skyscraper Elevator Ride

An elevator in a skyscraper starts from rest and moves straight up. Sensor data for one ride are shown in Table 1.

Table 1: Elevator Ride Data

Stage	Motion	Time (s)
1	Speeds up from 0 at 1.5 m/s²	4.0
2	Constant speed of 6.0 m/s	20.
3	Slows down to rest at 1.5 m/s²	4.0

What is the elevator’s total displacement for the ride?

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

Challenge score: 0 / 6

Substitute values

C1. Substitute numerical values into a mathematical representation that can be used to determine the elevator’s displacement during stage 1. Then calculate the displacement.

d = 12( m/s²)( s)² = m

Multiple choice

C2. Which graph best represents the elevator’s velocity versus time?

Draw the vector · Determine the magnitude

C3. During stage 3, choose the direction of the elevator’s acceleration and determine its magnitude.

elevator
●

a = m/s²

Support or Refute · Justify

C4. An engineer makes the following claim.

Claim: If the elevator’s top speed were doubled to 12 m/s, with the same 1.5 m/s² acceleration and slowing, the 144-m ride would take half as long (14 s).

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

Support Refute

Multiple choice

C5. Engineers want the same 144-m ride to take only 25 s, with the same top speed of 6.0 m/s and equal speeding-up and slowing-down times. What magnitude of acceleration is needed?

Constructed response

C6. The elevator is speeding up in stage 1 and slowing down in stage 3, yet its displacement is the same in both stages. Using the data in Table 1, explain why.

Word Problems →