A car goes from 10 to 20 m/s in 4 seconds. How far has it moved in that time?

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A car goes from 10 to 20 m/s in 4 seconds. How far has it moved in that time?

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Answer 1 · 2018-07-17T05:59:55

Car has moved $60 m$ $60m$ .

Explanation:

If initial velocity is $u$ $u$ and final velocity $v$ $v$ (at a uniform acceleration) in time $t$ $t$ ,

then acceleration $a$ $a$ is given by $v = u + a t$ $v=u+at$ i.e. $a = \frac{v - u}{t}$ $a=(v-u)/t$

and distance is given by $v^{2} - u^{2} = 2 a S$ $v^2-u^2=2aS$

Here $u = 10 \frac{m}{s}$ $u=10m/s$ , $v = 20 \frac{m}{s}$ $v=20m/s$ and $t = 4 s$ $t=4s$

which gives us $a = \frac{20 - 10}{4} = \frac{10}{4} = \frac{5}{2} \frac{m}{s^{2}}$ $a=(20-10)/4=10/4=5/2m/s^2$

Hence $2 \times \frac{5}{2} \times S = 20^{2} - 10^{2}$ $2xx5/2xxS=20^2-10^2$

or $5 S = 400 - 100 = 300$ $5S=400-100=300$

i.e. $S = \frac{300}{5} = 60 m$ $S=300/5=60m$

Additional information $-$ $-$ Another important relation is $S = u t + \frac{1}{2} a t^{2}$ $S=ut+1/2at^2$ and here $S = 10 \times 4 + \frac{1}{2} \times \frac{5}{2} \times 4^{2}$ $S=10xx4+1/2xx5/2xx4^2$

= $40 + 20 = 60 m$ $40+20=60m$

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A car goes from 10 to 20 m/s in 4 seconds. How far has it moved in that time?

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