Answer:
A. [tex]2\cdot t[/tex]
Explanation:
The SUV accelerates uniformly. In this case, speed ([tex]v[/tex]) is directly proportional to time ([tex]t[/tex]). That is:
[tex]v \propto t[/tex] (1)
[tex]v = k\cdot t[/tex]
Where [tex]k[/tex] is the proportionality constant.
Then, we eliminate this constant by creating the following relationship:
[tex]\frac{v_{1}}{t_{1}} = \frac{v_{2}}{t_{2}}[/tex] (2)
If we know that [tex]v_{1} = v[/tex], [tex]t_{1} = t[/tex] and [tex]v_{2} = 2\cdot v[/tex], then the time interval for the SUV to accelerate from rest to a speed [tex]2\cdot v[/tex] is:
[tex]\frac{v}{t} = \frac{2\cdot v}{t_{2} }[/tex]
[tex]t_{2} = 2\cdot t[/tex]
Hence, correct answer is A.
