Physics 1 — Motion & Energy

Motion with constant acceleration

ELI5: if your acceleration is steady, just two equations tell you everything:

The first is "speed builds at a steady rate"; the second adds up all those speeds over time.

v_{0} := 4 m/s

= 4 m / s initial velocity

a_{x} := 2 m/s^2

= 2 m / s^2 constant acceleration

t_{1} := 3 s

= 3 s elapsed time

v_{1} = v_{0} + a_{x} \cdot t_{1}

= 10 m / s velocity after t₁

d_{1} = v_{0} \cdot t_{1} + \frac{1}{2} \cdot a_{x} \cdot t_{1}^{2}

= 21 m distance covered

Real-world hook: this is the math of a car merging onto a highway, a plane's takeoff roll, and the 0–60 mph time in every car review.

Try it yourself: a car starts at 4 m/s and accelerates at 2 m/s² for 5 s. What is its final velocity? (v = v₀ + a·t.)

v_{final} := 4 m/s + 2 m/s^2 * 5 s

= 14 m / s ✏️ Your turn: compute v = 4 m/s + (2 m/s²)(5 s). Keep the unit on your answer (m/s).

✓ pass

abs(v_{final} - (4 m/s + 2 m/s^2 * 5 s)) < 0.01 m/s

green when your final velocity is correct