Translational Motion Flashcards
Speed and Velocity
Speed is change in distance over time (scalar)
Velocity is change in displacement over time (vector)
Acceleration
Acceleration is change in velocity over time (vector)
e.g. When objects fall (g = 10 m/s2), the object falls at 0 m/s at t = 0, 10 m/s at t = 1, 20 m/s t = 2, etc.
Uniformly Accelerated Motion - 3 Equations
No vt
No Δx
No t
Δx = v0Δt + 1/2a(Δt)2
Δv = aΔt
vt2 - v02 = 2aΔx
Height During Free Fall
Gravity
y = 1/2a(Δt)2
g = 10 m/s2
Free Fall Approximations
To get approximate velocity: multiply time by 10 (2.5 m/s at t = 0.25 s)
To get appoximate change in height: as drop time doubles, change in height quadruples (at t = 1 s, drops 5 m, at t = 2 s, drops 20 m)
Does horizontal motion affect vertical motion?
No. We can treat horizontal and vertical components seperately, making problem solving easier.
Time is independent of either processes, and can be calculated any which way.
Time to Top of Projectile
Total Time of Projectile
vty - v0y = gt
vty = 0 at top; v0y = -gt; ttop = v0y/(10 m/s2)
ttop = v0y/-g
ttotal will be twice the time it takes to get to the top
ttotal = 2v0y/g
Total Height of Projectile
vty2 - v0y2 = 2gΔh
vty = 0 at top; Δh = (-2v0y)2/2g
Δh = (-2v0y)2/2g
Total Range of Projectile
Dependent on inital and final height being the same
r = (2v0xv0y)/g
r= (v02sin(2θ))/g