Grade 12 · Week 03 · Monday · Day 01

Turning Changes Velocity

How can the speed remain steady while velocity changes?

Objective: Distinguish speed from vector velocity and explain why changing direction produces acceleration.

45–60 minutes · Offline-capable · Public practice is not a supervised examination

Read and reason

One speed, many velocities

Velocity has magnitude and direction. If a toy car moves along a circular path at steady speed, its velocity vector points along a changing tangent. Since velocity changes direction, the motion involves acceleration despite the speedometer staying constant. An acceleration can change speed, direction, or both. Our one-dimensional graph studio models changes in signed velocity magnitude, not complete circular paths.

Average acceleration is a change ratio

For one-dimensional motion, average acceleration ā = (v₂−v₁)/(t₂−t₁). Units are m/s². A car's velocity may go from +2 m/s to −2 m/s in two seconds; ā=(−2−2)/2=−2 m/s². Negative acceleration in the chosen coordinate system means velocity is becoming more negative. It does not always mean the object is slowing down.

Separate velocity from speed

Speed is |v| in a one-dimensional instantaneous model. A negative velocity of −4 m/s indicates motion toward decreasing position at a speed of 4 m/s. When velocity changes from −1 to −3 m/s, the object speeds up even though acceleration is negative. When velocity changes from +3 to +1 m/s under negative acceleration, it slows down. Determine speed change from absolute values, not the sign alone.

Why circular motion needs another model

Turning motion in a plane involves velocity components and acceleration perpendicular to velocity in uniform circular motion. A curved path cannot be represented fully with a single signed one-dimensional position value. Today use the familiar turning phenomenon to build a conceptual explanation, then analyze the strictly one-dimensional examples using v(t)=v₀+at. Do not mix up the two models' assumptions.

Vocabulary

acceleration
Rate of change of vector velocity; in one dimension a=Δv/Δt (m/s²). Explain with an original example.
speed
Nonnegative rate of travel; average speed = total distance/elapsed time (m/s). Explain with an original example.
velocity
Rate of signed position change; v = dx/dt, one-dimensional sign indicates direction (m/s). Explain with an original example.
vector
A quantity with both magnitude and direction; velocity is a vector. Explain with an original example.
direction
Orientation of motion, described as the sign in a one-dimensional axis model. Explain with an original example.

Worked example

Velocity goes from +6 m/s to +2 m/s in 2 s. Average acceleration=(2−6)/2=−2 m/s²; speed falls from 6 to 2 m/s. From −2 to −6 m/s in 2 s has the same −2 m/s² acceleration but increasing speed.

Check signs and units. Show each calculation rather than memorizing a number.

Your science journal

Explain the different roles of direction and magnitude. Give one example where a negative acceleration increases speed and one where it decreases speed.

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Daily Retrieval Practice · 4 Questions

Choose one answer to each question, check, read the feedback, and retry after correcting mistakes. Target 80% open-book mastery; public practice scores do not authenticate official midterms or finals.