An object is accelerating uniformly from 8.0 m/s to 16 m/s in 10 seconds. How far does the object travel in 10 seconds

acceleration, a = (16 - 8)/10 m/s² = 0.8 m/s².

 

Use v² = u² + 2as where v = final velocity, u = initial velocity, a = acceleration, s = distance.

Rearrange as:

s = (v² - u²)/(2a)

so

s = (16² - 8²)/(2*0.8) m

$${\mathtt{s}} = {\frac{\left({{\mathtt{16}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{{\mathtt{8}}}^{{\mathtt{2}}}\right)}{{\mathtt{1.6}}}} \Rightarrow {\mathtt{s}} = {\mathtt{120}}$$

s = 120m

 

Check:

You could also use s = ut + (1/2)at² where t is time.

s = 8*10 + (1/2)*0.8*10²m

$${\mathtt{s}} = {\mathtt{8}}{\mathtt{\,\times\,}}{\mathtt{10}}{\mathtt{\,\small\textbf+\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right){\mathtt{\,\times\,}}{\mathtt{0.8}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{2}}} \Rightarrow {\mathtt{s}} = {\mathtt{120}}$$

s = 120m

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