Answer :
Answer:
The magnitude of the acceleration of the car when [tex]s = 50\,m[/tex] is [tex]2\,\frac{m}{s^{2}}[/tex].
Explanation:
The acceleration can be obtained by using the following differential equation:
[tex]a = v \cdot \frac{dv}{ds}[/tex]
Where [tex]a[/tex], [tex]v[/tex] and [tex]s[/tex] are the acceleration, speed and distance masured in meters per square second, meters per second and meters, respectively.
Given that [tex]v = 0.2\cdot s[/tex], its first derivative is:
[tex]\frac{dv}{ds} = 0.2[/tex]
The following expression is obtained by replacing each term:
[tex]a = 0.2\cdot 0.2\cdot s[/tex]
[tex]a = 0.04\cdot s[/tex]
The magnitude of the acceleration of the car when [tex]s = 50\,m[/tex] is:
[tex]a = 0.04\cdot (50\,m)[/tex]
[tex]a = 2\,\frac{m}{s^{2}}[/tex]