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Answer:
[tex]12\; {\rm m\cdot s^{-1}}[/tex].
Explanation:
In this question, it is given that:
The goal is to find the velocity of the object after [tex]t = 5\; {\rm s}[/tex].
To find the new velocity, note that acceleration is the rate of change in velocity. An acceleration of [tex]a = (2/5)\; {\rm m\cdot s^{-2}}[/tex] means that velocity of the object increases by [tex](2/5)\; {\rm m\cdot s^{-1}}[/tex] every second. After [tex]t = 5\; {\rm s}[/tex], velocity would have increased by a total of:
[tex]\displaystyle a \, t = \left(\frac{2}{5}\; {\rm m\cdot s^{-2}}\right)\, (5\; {\rm s}) = 2\; {\rm m\cdot s^{-1}}[/tex].
This increase in velocity is in addition to the initial velocity of [tex]v_{0} = 10\; {\rm m\cdot s^{-1}}[/tex]. Hence, the actual velocity after [tex]t = 5\; {\rm s}[/tex] would be the sum of the original velocity and the increase from the acceleration:
[tex]\begin{aligned} v &= v_{0} + a\, t \\ &= 10\; {\rm m\cdot s^{-1}} + \left(\frac{2}{5}\; {\rm m\cdot s^{-2}}\right)\, (5\; {\rm s}) \\ &= 10\; {\rm m\cdot s^{-1}} + 2\; {\rm m\cdot s^{-1}} \\ &= 12\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].
In other words, the velocity of the object would be [tex]12\; {\rm m\cdot s^{-1}}[/tex] at [tex]t = 5\; {\rm s}[/tex].