Constant Acceleration

v = v_{0} + a t, s = s_{0} + v_{0} t + \frac{1}{2} a t^{2}, v^{2} = v_{0}^{2} + 2 a (s - s_{0})

When acceleration is constant, the three handbook kinematic equations relate position, velocity, and time. Free-fall uses a = g (sign by your coordinate system).

$v_{0}$ (m/s): Initial velocity
$a$ (m/s²): Constant acceleration
$s$ (m): Position

Step-by-step solved example

A car accelerates from 10 m/s at 2 m/s². Speed after 80 m?

Straight-line kinematics — the same distance split used later in SSD.

1. No-time equation
v² = 10² + 2(2)(80) = 100 + 320 = 420.
$v = 420 = 20.5 m/s$

Answer: 20.5 m/s

10 practice questions

0/10 correct

1.From rest, a = 3 m/s² for 4 s. v =

2.Distance from rest at 4 m/s² in 3 s is

3.v = 20 m/s, v0 = 0, s = 50 m. a =

4.Free-fall 2 s from rest (g = 9.81): speed ≈

5.A projectile’s horizontal acceleration (no drag) is

6.Stopping distance from 30 m/s at −6 m/s² is

7.Average velocity with const a from 4 to 10 m/s is

8.Units of acceleration are

9.s = 5 + 8t + t² (SI). Acceleration is

10.Time to travel 100 m from rest at 5 m/s² is