Solving Word Problems - Kinematics

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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

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

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

↓

Step 3 — Substitute and Solve

Δd = V_it + ½aΔt²

= 0 m/s(4 sec) + ½(10 m/s²)(4 sec)²

Δd = 0 + 5(16)

Δd = 80 m

D. Deriving the 2nd Displacement Equation

Goal

V_f² = V_i² + 2aΔd

Start with

Δd = VΔt where V = (V_f + V_i)/2

Since V_f = V_i + aΔt, then Δt
= (V_f − V_i)/a

Δd = [(V_f + V_i)/2] · [(V_f − V_i)/a]

Cross multiply

2aΔd = V_f² − V_i²

Rearrange

V_f² = V_i² + 2aΔd

Wheelchair basketball player bouncing a ball

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

V_i = 6 m/s a = 2 m/s² V_f = ? d = 7 m

↓

Step 3 — Substitute and Solve

V_f² = V_i² + 2aΔd

= (6 m/s)² + 2(2 m/s²)(7 m)

V_f² = 36 + 4(7) = 64

V_f = 8 m/s

Check Your Understanding

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

1. A car accelerates uniformly from rest at +4 m/s². How far does it travel in 5 s?

2. A car moving at +3 m/s accelerates at 2 m/s² over 4 m. What is its final velocity?

3. An object has a negative velocity and a positive acceleration. What is it doing?

4. In a word problem, "starts from rest" tells you that...

5. Which equation lets you find final velocity WITHOUT knowing the time?

Displacement Plots →

Bonus

Ever see an object roll UP hill?