SUVAT Velocity — Accelerating Train (Worked Example)

Easy

Problem

A high-speed train passes a signal at 15 m/s and accelerates uniformly at 0.8 m/s² for 20 s. What is its speed at the end of this interval?

Given

u = 15 m/s
a = 0.8 m/s²
t = 20 s

Find

The final velocity v.

Principle

Constant acceleration adds the same velocity increment every second. The SUVAT equation v = u + at combines the starting velocity with the total gain.

Formula

v = u + at

v = u + at

Solution

Write the equation: $v = u + at$
Substitute: $v = 15 + (0.8)(20)$
The gained velocity is $0.8 \times 20 = 16\ \mathrm{m/s}$
Add: $v = 15 + 16 = 31\ \mathrm{m/s}$

31 m/s

Unit check

m/s² × s = m/s, added to m/s. All terms are velocities — consistent.

What this means physically

31 m/s is about 112 km/h. The train is still well below cruising speed, which is why real trains accelerate for several minutes — gentle acceleration over long times builds high speed.

Common mistake

Adding numbers with mismatched units, e.g. treating the 20 s as a velocity. Always check that a×t has velocity units before adding it to u.