Respuesta :
The definition of average acceleration allows to find the result for the average acceleration in the given time interval is:
[tex]a_{average}= 1.5 \ \frac{m}{s^2}[/tex]
Instantaneous acceleration is defined as the derivative of velocity with respect to time.
a = [tex]\frac{dv}{dt}[/tex]
Where a is the acceleration, v the velocity and t the time.
They indicate that the speed of the car is given by the relation.
v = α t + β t²
With α = 3 m / s and β = 0.1 m / s³
Let's make the derivative.
a = α + 2β t
Let's substitute
a = 3 + 2 0.1 t
Average acceleration is the change in velocity in the time interval.
[tex]a_{average} = \frac{\Delta v}{\Delta t }[/tex]
Let's find the velocity at the indicated time.
For t = 5 s
v₅ = 3 + 0.1 5²
v₅ = 5.5 m / s
For t = 10 s
v₁₀ = 3 + 0.1 10²
v₁₀ = 13 m / s
Let's calculate the average acceleration.
[tex]a_{average} = \frac{13 - 5.5 }{ 10 - 5 }\\[/tex]
[tex]a_{average}= 1.5 \ m/s^2[/tex]
In conclusion using the definition of mean acceleration we can find the result for the mean acceleration in the given time interval is:
[tex]a_{average} =[/tex] 1.5 m / s²
Learn more here: brainly.com/question/20057878
