The relationship between acceleration and time a(t) for the model rocket v(t)=αt³ + βt + γ, where α=−3. 0m/s4, β=36m/s2, and γ=1. 0m/s is a(t) = -9t² + 36 m/s²
The differentiation of velocity with respect to time gives acceleration.
Velocity of a rocket model is the speed acquired of the body in a particular direction.
Acceleration of the body is the change in velocity with respect to time.
v(t)=αt³ + βt + γ
On differentiating,
a = 3αt² + β
Given, α=−3. 0m/s⁴
β=36m/s²
γ=1. 0m/s
On subsituting,
a = 3(-3)t² + 36 m/s²
Hence, relationship between acceleration and time a(t) = -9t² + 36 m/s²
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