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 3 years ago
a car is traveling in a straight line and decelerating at a constant rate. after 3.2 s it traveled 88m and slowed to a speed of 17m/s what was the initial speed of the car?
 3 years ago
a car is traveling in a straight line and decelerating at a constant rate. after 3.2 s it traveled 88m and slowed to a speed of 17m/s what was the initial speed of the car?

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nikvist
 3 years ago
Best ResponseYou've already chosen the best response.0\[t=3.2s\quad,\quad s=88m\quad,\quad v=17m/s\]\[v=v_0at\quad\Rightarrow\quad a=\frac{v_0v}{t}\]\[v^2=v_0^22as=v_0^22\frac{v_0v}{t}s=v_0^2\frac{2s}{t}v_0+\frac{2s}{t}v\]\[v_0^2\frac{2s}{t}v_0+\frac{2s}{t}vv^2=0\]\[v_0=\frac{\frac{2s}{t}\pm\sqrt{\left(\frac{2s}{t}\right)^24\left(\frac{2s}{t}vv^2\right)}}{2}=\]\[=\frac{s}{t}\pm\sqrt{\left(\frac{s}{t}\right)^2\frac{2s}{t}v+v^2}=\frac{s}{t}\pm\sqrt{\left(\frac{s}{t}v\right)^2}=\]\[=\frac{s}{t}\pm\left(\frac{s}{t}v\right)\quad\mbox{(only sign +)}\]\[v_0=\frac{2s}{t}v=38m/s\]

shubham
 3 years ago
Best ResponseYou've already chosen the best response.2OR Use this equation of motion S = {(u+v)/2}t 88m = {(u+17)/2}3.2 u=5513 = 38m/s

shubham
 3 years ago
Best ResponseYou've already chosen the best response.2For constant accelarations, velocity is linear function of time and hence you can assume mean of initial and final velocities to be the average velocity. So, you don't need a actually.

AJTurnbull
 3 years ago
Best ResponseYou've already chosen the best response.0oh that makes it easy been trying to figure that out all night
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