How Fast, Which Way

Why it matters

Two trains do a steady 40 km/h. A physicist swears they have completely different velocities. The trains face each other, and the physicist is right.

The idea in plain words

The vocabulary of fast. Tap the terms.

speed = distance/time · velocity = displacement/time

A car covers 100 km in 2 h, then rests 30 min, then 50 km in 30 min. Average speed?

50 km/h

• m/s: average speed — total distance ÷ total time — what the odometer and clock say
• m/s: instantaneous speed — the speedometer's RIGHT-NOW reading
• the strict club: uniform velocity — equal displacements in equal intervals — constant speed AND unchanging direction
• the classic trap: circular track — constant SPEED but ever-changing velocity — direction turns even when the number doesn't
• total distance = 150 km
• total time = 3 h (rest counts!)

Predict first

Two trains run at 40 km/h toward each other. They have…

Velocity = speed + direction. East at 40 and west at 40 are as different as +40 and −40.

• equal speeds but different (opposite) velocities — correct
• equal velocities
• different speeds

What you do

Drive train B: match speeds with opposite velocity, then same direction with a different speed.

Check yourself

A car on a circular track at steady 60 km/h has…

The direction rotates continuously — velocity changes every instant, and that (next chapter) means acceleration.

Average VELOCITY of any complete round trip is…

displacement/time with zero displacement = 0, however hard you drove. Average SPEED stays healthy.

m/s to km/h: multiply by…

10 m/s = 36 km/h. (km/h → m/s is the 5/18 direction.)

• constant speed, changing velocity — correct
• constant velocity
• changing speed
• zero — displacement is zero — correct
• the same as average speed
• negative
• 18/5 (= 3.6) — correct
• 5/18
• 60