Kinematics

Word Problems

Solving With The GUESS Method

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Do Now warm-up prompt

Word Problems — solving constant-acceleration problems with the GUESS method

Warm-Up

An object has a negative velocity and a positive acceleration. Is it speeding up or slowing down?

Video Instruction

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C. Solving Word Problems

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Ex 1

A car accelerates uniformly from rest at a rate of +10 m/s². How far will the car travel in 4 seconds?

Step 1 — Read and underline all the important information

Step 2 — Turn all your information into letters

Given

Vi = 0 (starts from rest)   a = +10 m/s²   t = 4 sec   d = ?

↓

Step 3 — Substitute and Solve

GUESS method equation reference chart

Δd = Vit + ½aΔt²

= 0 m/s(4 sec) + ½(10 m/s²)(4 sec)²

Δd = 0 + 5(16)

Δd = 80 m

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D. Deriving the 2nd Displacement Equation

Goal

Vf² = Vi² + 2aΔd

Start with

Δd = VΔt   where   V = (Vf + Vi)/2

Since Vf = Vi + aΔt, then Δt = (Vf − Vi)/a

Δd = [(Vf + Vi)/2] · [(Vf − Vi)/a]

Cross multiply

2aΔd = Vf² − Vi²

Rearrange

Vf² = Vi² + 2aΔd

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Ex 2

A car with an initial velocity of +6 m/s accelerates at a rate of 2 m/s². Find the car's final velocity after it travels 7 m from its initial position.

Step 1 — Read and underline all the important information

Step 2 — Turn all your information into letters

Given

Vi = 6 m/s   a = 2 m/s²   Vf = ?   d = 7 m

↓

Step 3 — Substitute and Solve

GUESS method equation reference chart

Vf² = Vi² + 2aΔd

= (6 m/s)² + 2(2 m/s²)(7 m)

Vf² = 36 + 4(7) = 64

Vf = 8 m/s

Displacement Plots →

Bonus

Ever see an object roll UP hill?