+0  
 
0
1510
7
avatar

A boat takes off from the dock at 2.5 m/s and speeds up at 4.2 m/s2 for 6.0 s. How far has the boat traveled? Round your answer to the nearest whole number.

Guest Jan 14, 2016

Best Answer 

 #5
avatar+92775 
+15

Hi guest and Solveit,
 

A boat takes off from the dock at 2.5 m/s and speeds up at 4.2 m/s2 for 6.0 s. How far has the boat traveled? Round your answer to the nearest whole number.

 

Your formula is incorrect guest sad .    The one you are thinking of is   v=u+at

u=2.5m/s,     a=4.2m/s^2      t=6s,      find s

The one you need is

 

\(s=ut+0.5at^2\\ s=2.5*6+\frac{1}{2}*4.2*36\\ s=15+2.1*36\\ s=90.6\; metres.\)

 

When I was at school I did both maths and physics.  

Now in physics I used the physics formulas    BUT     in maths ir was compulsory to use calculus!

So now I will do it with calculus.

 

\(x\; is \;displacement,\;\;\\\frac{dx}{dt}\;\;is \;velocity\;\;\;\\\frac{d^2x}{dt^2}\;\;is \;acceleration\;\;\;and\;\\t\;is\;time.\\ \)

 

\(\frac{d^2x}{dt^2}=4.2\\ \frac{dx}{dt}=4.2t+c_1\\ when\;t=0\;\;\frac{dx}{dt}=2.5\\ \quad sub\; in\\ 2.5=4.2*0+c_1\\ c_1=2.5\\ \frac{dx}{dt}=4.2t+2.5\\ x=\frac{4.2t^2}{2}+2.5t+c_2\\ \mbox{When t=0, x=0 so }c_2=0\\ x=\frac{4.2t^2}{2}+2.5t\\ When \; t=6\\ x=2.1*6^2+2.5*6\\ x=90.6\;metres \)

 

 

That is how you do it using calculus    laugh

Melody  Jan 15, 2016
 #1
avatar+2493 
0

i think:

4.2-2.5 = 1.7      2.5+0.85 = 3.35 it is his avareage speed

 

3.35*6 = 20.1

 

the answer: 20

Solveit  Jan 14, 2016
 #2
avatar
+5

Simple SUVAT problem,

 

S = u + at
S = 2.5 + 4.2*6

S = 27.2 meters

Guest Jan 14, 2016
 #3
avatar+2493 
0

doesn t it saying that initial speed was 2.5 and it speeded up to 4.2 in 6s 

Solveit  Jan 14, 2016
 #4
avatar
0

By the units given, the initial speed is 2.5 ms^-1 where it's acceleration is 4.2 ms^-2.

Guest Jan 14, 2016
 #5
avatar+92775 
+15
Best Answer

Hi guest and Solveit,
 

A boat takes off from the dock at 2.5 m/s and speeds up at 4.2 m/s2 for 6.0 s. How far has the boat traveled? Round your answer to the nearest whole number.

 

Your formula is incorrect guest sad .    The one you are thinking of is   v=u+at

u=2.5m/s,     a=4.2m/s^2      t=6s,      find s

The one you need is

 

\(s=ut+0.5at^2\\ s=2.5*6+\frac{1}{2}*4.2*36\\ s=15+2.1*36\\ s=90.6\; metres.\)

 

When I was at school I did both maths and physics.  

Now in physics I used the physics formulas    BUT     in maths ir was compulsory to use calculus!

So now I will do it with calculus.

 

\(x\; is \;displacement,\;\;\\\frac{dx}{dt}\;\;is \;velocity\;\;\;\\\frac{d^2x}{dt^2}\;\;is \;acceleration\;\;\;and\;\\t\;is\;time.\\ \)

 

\(\frac{d^2x}{dt^2}=4.2\\ \frac{dx}{dt}=4.2t+c_1\\ when\;t=0\;\;\frac{dx}{dt}=2.5\\ \quad sub\; in\\ 2.5=4.2*0+c_1\\ c_1=2.5\\ \frac{dx}{dt}=4.2t+2.5\\ x=\frac{4.2t^2}{2}+2.5t+c_2\\ \mbox{When t=0, x=0 so }c_2=0\\ x=\frac{4.2t^2}{2}+2.5t\\ When \; t=6\\ x=2.1*6^2+2.5*6\\ x=90.6\;metres \)

 

 

That is how you do it using calculus    laugh

Melody  Jan 15, 2016
 #6
avatar+87294 
+5

Nice, Melody......it's interesting to see how the Physics "formulas" can be derived using Calculus.......

 

 

cool cool cool

CPhill  Jan 15, 2016
 #7
avatar+92775 
0

Thanks Chris :D  

Melody  Jan 15, 2016

11 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.