Answer:
The velocity of the object 7 seconds from the start of its journey is 70 ms⁻¹.
Explanation:
To find the velocity of the object after 7 seconds after the start of its journey, we first needs to consider the acceleration of the object in the each part of the motion: the initial 2 seconds and the subsequent 4 seconds.
First leg of journey
As we have been given the displacement (s), the initial velocity (u), the final velocity (v) and the time (t), we can use the following SUVAT equations to find the acceleration (a) and the final velocity (v) of the object during the first leg of its journey (initial 2 seconds):
[tex]\textsf{Given:} \quad s=20\;\textsf{m}, \quad u=0\;\textsf{ms}^{-1}, \quad t=2\;\textsf{s}[/tex]
[tex]\begin{aligned}\textsf{Using:} \quad s&=ut+\dfrac{1}{2}at^2\\\\\implies 20&=0(2)+\dfrac{1}{2}a(2^2)\\20&=2a\\a&=10\; \sf ms^{-2}\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Using:} \quad v&=u+at\\\\\implies v&=0+10(t)\\v&=20\; \sf ms^{-1}\end{aligned}[/tex]
Therefore, the acceleration of the object for the initial 2 seconds of its journey is 10 ms⁻² and its final velocity is 20 ms⁻¹.
Second leg of journey
The initial velocity of the second leg of the journey is equal to the final velocity of the previous leg of the journey. Therefore, as we have been given the displacement (s) and the time (t), and have calculated the initial velocity (u), we can use the following SUVAT equation to find the acceleration (a) of the object during the second leg of its journey (next 4 seconds):
[tex]\textsf{Given:} \quad s=160\;\textsf{m}, \quad u=20\;\textsf{ms}^{-1}, \quad t=4\;\textsf{s}[/tex]
[tex]\begin{aligned}\textsf{Using:} \quad s&=ut+\dfrac{1}{2}at^2\\\\\implies 160&=20(4)+\dfrac{1}{2}a(4^2)\\160&=80+8a\\8a&=80\\a&=10\; \sf ms^{-2}\end{aligned}[/tex]
Therefore, the acceleration of the object for the next 4 seconds of its journey is 10 ms⁻².
We can observe that the acceleration for both legs of the journey is the same, and so the object is moving with constant acceleration of 10 ms⁻².
Velocity after 7 seconds
Assuming the acceleration remains constant through the entire journey of the object, to calculate the velocity of the object after 7 seconds from the start, use the following SUVAT equation:
[tex]u=0\; \textsf{ms}^{-1}, \quad a=10\;\textsf{ms}^{-2}, \quad t=7\;\textsf{s}[/tex]
[tex]\begin{aligned}\textsf{Using:} \quad v&=u+at\\\\\implies v&=0+10(7)\\v&=70\; \sf ms^{-1}\end{aligned}[/tex]
Therefore, the velocity of the object 7 seconds from the start of its journey is 70 ms⁻¹.
