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Sagot :
ANSWER
0. a = 20.66 cm/s^2
,1. a = 20.66 cm/s^2
,2. t = 2.60 s
EXPLANATION
1. The initial speed in release 1 is zero. The distance the cart travels is x = 200cm
Which we can write as a function of time:
[tex]x=x_0+v_0t+\frac{1}{2}at^2[/tex]We know that the cart traveled for 4.40 seconds. Replacing with the information we have:
[tex]\begin{gathered} 200cm=0+0\cdot4.40s+\frac{1}{2}a\cdot4.40^2s^2 \\ 200cm=\frac{1}{2}\cdot a\cdot4.40^2s^2 \end{gathered}[/tex]Solving for a:
[tex]a=\frac{2\cdot200cm}{4.40^2s^2}=20.66cm/s^2[/tex]The magnitude of the cart's acceleration is 20.66 cm/s^2, rounded tot he nearest hundredth.
2. Now the students wants the cart to travel x = 70 cm instead. If it is the same cart and the same ramp, with the same slope, then the forces acting upon the cart are the same. This means that it doesn't matter from what position of the ramp the cart is released, it will have the same acceleration every time. However in this case, it will travel for a shorter period of time.
Hence the acceleration in release 2 is the same as in release 2: 20.66 cm/s^2
3. In this case we know that x = 70cm, a = 20.66 cm/s^2 and we have to find t. From this formula:
[tex]x=x_0+v_0t+\frac{1}{2}at^2[/tex]Replacing with the information we have:
[tex]70\operatorname{cm}=\frac{1}{2}\cdot20.66\operatorname{cm}/s^2\cdot t^2[/tex]And solving for t:
[tex]t=\sqrt[]{\frac{70\operatorname{cm}\cdot2}{20.66\operatorname{cm}/s^2}}=2.60s[/tex]We find that the cart traveled for 2.60 seconds, rounded to the nearest hundredth.
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