Motion with calculus formulas

Use when x = A + Bt + Ct² + Dt³. B, C, D = the numbers in front of t, t², t³. Missing term: 0. Keep minus signs. Position at time t: type x(t) on the home screen with your t, like 5−12(2)+2(2)³. Given v(t)? Put its t, t², t³ numbers in B, C, D (skip its plain number): answer is a (m/s²). Leave t empty to find when v hits a value (v = 0: it stops or turns). 2-D: do x and y one at a time, then speed = √(vₓ² + vᵧ²).

Use when x = A + Bt + Ct² + Dt³. C, D = the numbers in front of t², t³. Missing term: 0. Keep minus signs. No t³ term: a = 2C at every time. Given v(t)? Use v = B + 2Ct + 3Dt² with B, C, D = v(t)'s t, t², t³ numbers: answer is a. 2-D: do x and y one at a time, then size = √(aₓ² + aᵧ²).

Use when a = A + Bt + Ct². A = plain number, B and C = numbers in front of t and t². Missing term: 0. v₀ = velocity at t = 0 (from rest: 0). Know v at another time? Leave v₀ empty first. Given v(t), want x? A, B, C = v(t)'s plain, t, t² numbers; x₀ (or 0) in v₀: answer is x (m). Δx from t₁ to t₂: do t₂, then t₁, subtract. Find t (a(t) has no t²): in v = B + 2Ct + 3Dt² type B = v₀, C = A/2, D = (a(t)'s t number)/6.