Why am I getting wrong value here?

Question

A man threw a ball with force 10 N to two displacement of 5 m and 10 m.

F = ma, so let mass be 2 kg.
a = 5 m/s2.

Work done = 10 × 5 and 10 × 10 = 50 Nm and 100 Nm.
Now, since a = 5, I assumed that after 5 m velocity = 25 [m/s].
Now, when I do K.E f - K.E initial for final work done i.e 50 Nm for now.

Initial K.E. = 0.

So , then K.E final is not equal to work done final.
25 × 25 is not equal to 50 Nm.
Where am I wrong?

NMech · Accepted Answer

The mistake is in your assumption.
Now, since a = 5, I assumed that after 5 m velocity = 25 m/s.
the correct would have been
Now, since a = 5, I assumed that after 5 [s] velocity = 25 m/s.
The way you can calculate it is from the following form of the equation for acceleration:
$$a = u frac{du}{ds}$$
you can obtain that $acdot 5m = frac{u_{out}^2}{2} rightarrow u_{out} = sqrt{2 cdot acdot 5[m]}$.
The rest I leave to you.

Why am I getting wrong value here?

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