The magnitude of the car's acceleration is 2.45 m/[tex]\rm sec^2[/tex] and this can be determined by using the equation of kinematics.
Given :
According to the kinematics:
[tex]\rm v = u + at[/tex] --- (1)
where v is the final speed, u is the initial speed, a is the acceleration and t is time.
Now, put the known terms in equation (1).
0 = 7 + at
at = -7
[tex]\rm t = -\dfrac{7}{a}[/tex] --- (2)
From the kinematics the displacement is given by the equation:
[tex]\rm S =ut+\dfrac{1}{2}at^2[/tex]
Now, put the values of u, S, and t in the above equation.
[tex]10=7\times \dfrac{-7}{a}+\dfrac{1}{2}\times a \times \dfrac{49}{a^2}[/tex]
Now, simplify the above equation.
[tex]10=-\dfrac{49}{a}+\dfrac{49}{2a}[/tex]
20a = -49
a = -2.45
So, the magnitude of the car's acceleration is 2.45 m/[tex]\rm sec^2[/tex].
For more information, refer to the link given below:
https://brainly.com/question/7590385
