Physics

A car travels 60 m east in 4.0 s, then 20 m west in 2.0 s. What is its average velocity for the whole trip?

Average velocity = total displacement / total time. Displacement = 60 m E − 20 m = 40 m east. Time = 6.0 s. v = 40 m / 6.0 s = 6.7 m/s east. (Average SPEED would be 80 m / 6.0 s = 13 m/s — different, because speed uses total distance.)

Distinguish distance from displacement and speed from velocity.

Distance and speed are scalars (magnitude only); displacement and velocity are vectors (magnitude AND direction). Displacement is the straight-line change in position; over a closed loop displacement is zero even though distance traveled is not.

An object starts from rest and accelerates uniformly at 3.0 m/s² for 5.0 s. How far does it travel?

Use x = v₀t + ½at². With v₀ = 0: x = ½(3.0)(5.0)² = ½(3.0)(25) = 37.5 m ≈ 38 m. (Check via v = at = 15 m/s; average velocity = (0+15)/2 = 7.5 m/s; x = 7.5 × 5.0 = 37.5 m.)

State the four standard kinematic equations for constant acceleration.

v = v₀ + at; x = x₀ + v₀t + ½at²; v² = v₀² + 2a(x − x₀); x = x₀ + ½(v₀ + v)t. They apply ONLY when acceleration is constant.

A ball is thrown straight up at 20 m/s. Taking g = 10 m/s², how high does it rise and how long until it returns to the thrower's hand?

At the top v = 0. Using v² = v₀² − 2gh: 0 = 20² − 2(10)h → h = 400/20 = 20 m. Time up: v = v₀ − gt → 0 = 20 − 10t → t = 2.0 s; total flight = 4.0 s (symmetric).