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

Guest Dec 18, 2014

#1**+5 **

acceleration, a = (16 - 8)/10 m/s^{2} = 0.8 m/s^{2}.

Use v^{2} = u^{2} + 2as where v = final velocity, u = initial velocity, a = acceleration, s = distance.

Rearrange as:

s = (v^{2} - u^{2})/(2a)

so

s = (16^{2} - 8^{2})/(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)at^{2 }where t is time.

s = 8*10 + (1/2)*0.8*10^{2}m

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

s = 120m

.

Alan
Dec 18, 2014

#1**+5 **

Best Answer

acceleration, a = (16 - 8)/10 m/s^{2} = 0.8 m/s^{2}.

Use v^{2} = u^{2} + 2as where v = final velocity, u = initial velocity, a = acceleration, s = distance.

Rearrange as:

s = (v^{2} - u^{2})/(2a)

so

s = (16^{2} - 8^{2})/(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)at^{2 }where t is time.

s = 8*10 + (1/2)*0.8*10^{2}m

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

s = 120m

.

Alan
Dec 18, 2014