Acceleration

The question

Astronauts orbit Earth at 28,000 km/h and float, weightless. You sit still and feel your chair push up on you. Huge speed gives weightlessness; zero speed gives weight. So whatever your body senses, it isn't speed. What is it?

What you feel in a launching rocket or a braking bus is acceleration — the rate your velocity changes — not speed itself. Cruise at a steady velocity and you feel nothing; the instant it changes, you feel a force.

The key idea

Acceleration measures how quickly velocity changes. Going 0 to 30 m/s in 3 s gains 10 m/s every second; the same change over 15 s gains only 2 m/s per second — far gentler. You divide the change in velocity by the time it took.

The unit m/s² means 'm/s of speed gained each second'. A negative value (deceleration) means velocity is dropping. Near Earth, gravity gives everything $9.8\,\text{m/s}^2$ downward. The rearrangements matter too: $\Delta v = a\cdot \Delta t$ and $\Delta t = \Delta v/a$. The Newton's Second Law tab links this to its cause — a = F_net/m, so the same net force gives a smaller acceleration on a larger mass. **Limiting case:** $a = 0$ is not 'stopped' — it is unchanging velocity, the first-law limit; and constant $a$ is exactly a straight-line v–t graph, the only case the suvat equations cover. **Connect it:** $a$ is the slope of the v–t graph, and multiplying it by mass turns kinematics into dynamics: $F = ma$ — measure the slope, and you have measured the net force per kilogram.

The formula

• ·a = acceleration in metres per second squared (m/s²)
• ·Δv = final velocity − initial velocity (m/s)
• ·Δt = the time interval (s). The Δ ('delta') means 'change in'
• ·so always subtract the starting value first.

What to remember

• ·Acceleration = change in velocity ÷ time, in m/s².
• ·Constant velocity (even a large one) means zero acceleration.
• ·Slowing down is acceleration opposite to the motion (negative).