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We know $S=ut+1/2at^2$. Now, let's say my initial velocity is $u=10\text { m/s}$ and acceleration $a=5\text{ m/s}^2$.

In first second distance traveled $S^{t=1}=10\text { m}$ as my speed is $10\text{ m/s}$ and time is $1 \text{ s}$.

In next second my speed will be $15m/s$ as $a=5m/s^2$and distance travelled will be $S^{_t=2}=S^{_t=1} + 15=25m$ as distance traveled in 2nd second is $15m$.

Now when I apply the same case in equation $S=ut+1/2at^2$ where $u=10m/s$, $a=5m/s^2$ and $t=2s$ I get $S=30m$

Where Iam I getting wrong?

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  • $\begingroup$ Suppose you're travelling at a constant speed of 10 m/s, then after the first second you travel a distance of 10 m. Right. But if you're accelerating then during that first second your speed will increase above 10 m/s and therefore you will travel more than 10 m. $\endgroup$
    – lemon
    Commented Mar 9, 2016 at 16:50
  • $\begingroup$ Hello and Welcome to Stack Exchange. Note that we are not a homework help-site and check-my-work questions are generally off-topic. That said, the problem is that your first idea (first second/second second) doesn't take into account that the speed is NOT 10 m/2 for the whole second, but gradually increases. $\endgroup$
    – Martin
    Commented Mar 9, 2016 at 16:52

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In the first second, the distance you traveled is your mean velocity x 1s. That is: (10m/s + 15m/s)/2, so you travel 12.5m.

(*) uniform acceleration implies that Mean velocity = (initial velocity + final velocity)/2

In the next second, your mean velocity is (15m/s + 20m/s)/2, sou you travel 17.5m.

12.5m + 17.5m = 30m

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