Acceleration Formulas

Formulas ∆ v = a ∆t change in v ~ time (uniform acceleration) v 2 − v 1 = a (t 2 − t 1 ) (time when) v 2 = v 1 + at (elapsed time) Solving for a: a = (v 2 − v 1 ) / t Solving for t: t = (v 2 − v 1 ) / a

Formulas v 2 = v 1 + at v average = v̄ = ½ (v 1 + v 2 ) distance = s = ∆x = x 2 − x 1 = v̄ t s = ½ (v 1 + v 2 ) t s = ½ (v 1 + v 1 + at) t s = v 1 t + ½ at 2

More Formulas Algebra Review: (x + y )∙(x – y ) f o i l = x² – xy + xy – y² = x² – y² a = (v 2 – v 1 )/t s = ½(v 2 +v 1 )∙t (average velocity) ∙ time Multiply : as = ½(v 2 ² –v 1 ²)  2as = v 2 ² –v 1 ²

Basic Formulas a = (v 2 − v 1 ) / t v̄ = ½ (v 1 + v 2 ) s = v̄ t Advanced Formulas s = v 1 t + ½ at 2 2as = v 2 ² –v 1 ²

Prob Set 4: 9 An arrow is shot straight up with a speed of 40 m/s. Three seconds later it hits a bird. How fast was the arrow going when it hit the bird ? g = −10 m/s 2 t = 3 s v 0 = 40 m/s v 1 = v 0 + a⋅t = 40m/s – 10m/s 2 ⋅ 3s = 40m/s – 30m/s = 10 m/s How high was the bird ? s = v̅ t = ½ (40+10) ⋅t = 25m/s ⋅ 3 s = 75 m

Suppose the Distance is Given The arrow is shot with a speed of 40 meters per second. The bird is 50 meters up. How fast was the arrow going when it hit the bird ? g = −10 m/s 2 s = 50 m t = ? v 1 = 40 m/s v 2 = v 1 + a ⋅ t Won’t work 2as = v 2 ² – v 1 ²  v 2 is unknown v 2 ² = v 1 ² + 2as = 40² + 2 ⋅ ( – 10) ⋅ 50 = 1600 – 1000 = 600 v 2 = √600 = 24.5 m/s up or 24.5 m/s down