A car moving in the x direction has acceleration aₓ, that varies with time as shown in the figure

A car moving in the x direction has acceleration aₓ, that varies with time as shown in the figure. pic.twitter.com/xLnJUtQIyp

— Physics I (@PHY210) September 28, 2016

If a (t) is acceleration and a (t) = a₀ + bt, where a₀ and b are constants, and t is the time

If a (t) is acceleration and a (t) = a₀ + bt, where a₀ and b are constants, and t is the time.

v (t) = v₀ + a₀t + bt² / 2

x (t) = x₀ + v₀t + a₀t² / 2 + bt³ / 6

x (t₁) = x₀ + v₀t₁ + a₀t₁² / 2 + bt₁³ / 6

x (t₂) = x₀ + v₀t₂ + a₀t₂² / 2 + bt₂³ / 6

x (t₂) - x (t₁) = v₀ (t₂ - t₁) + a₀ (t₂² - t₁²) / 2 + b (t₂³ - t₁³) / 6