Centripetal Acceleration — Car on a Curve (Worked Example)

Medium

Problem

A car rounds a curve of radius 50 m at a steady 20 m/s. What is its centripetal acceleration?

Given

v = 20 m/s
r = 50 m

Find

Centripetal acceleration a.

Principle

Turning at constant speed is still acceleration — velocity's direction changes, requiring a = v²/r toward the centre.

Formula

a = \frac{v^2}{r}

a = v²/r

Solution

Write the formula: $a = v^2/r$
Substitute: $a = 20^2 / 50$
Calculate: $a = 400 / 50 = 8\ \mathrm{m/s^2}$

8 m/s² toward the centre of the curve

Unit check

(m/s)² ÷ m = m/s² — correct.

What this means physically

8 m/s² is 0.82g sideways — you feel pressed against the door. Tyre friction must supply this; on ice (low friction) the car cannot hold the turn.

Common mistake

Calling it centrifugal and pointing it outward. The real acceleration points inward — 'centrifugal' is the feeling in the car's frame, not a real force.