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kinematic-1D.md

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Kinematics 1D

  1. Skipped

  2. Car moves 50m in 5s a. $\displaystyle v = \frac{m}{s} = \frac{50}{2} = 10\frac{m}{s}$ b. Aufgabe 2B c. Bei der Hälfte

  3. Sportscar accelerates in 3rd gear from $48.3 km/h$ to $80.5 km/h$ within $3.7s$

    1. How big is his average acceleration?
      • $\delta v = v_E - v_A = 80.5km/h - 48.3km/h = 32.2km/h$
      • $a = \frac{v_E - v_A}{t} = \frac{(80.5km/h - 48.3km/h)/3.6}{3.7s} = \underline{\underline{2.42m/s}}$
    2. How fast would it be, if it accelerated at that pace for an hour?
      • $1h = 3600s$
      • $80.5km/h / 3.6 = 22.36m/s$
      • $\displaystyle v_E = v_A + a_m * t = 22.36m/s + 2.42m/s * 3600s = \underline{\underline{8725 m/s}}$

  4. Car starts from standing. Endspeed is $30m/s$, drives for $10s$.

    1. How far did it drive?
      • $\overline{v} = v_E / 2 = 30m/s / 2 = 15m/s$
      • $s_Auto = \overline{v} * t = 15m/s * 10s = \underline{\underline{150m}}$

  5. Car starts from standing. Constant acceleration of $1m/s^2$.

    1. Which distance $s$ did the car cover, if it's end velocity $v_E$ is $5 m/s$
    • $\displaystyle s=\frac{v_E^2-v_A^2}{2a}=\frac{5^2m/s}{2m/s^2}=\frac{25m/s}{2m/s^2}=\underline{\underline{12.5m}}$

  6. Car starts from standing. Starts $10m$ behind the origin and reaches $60m$ in $10s$

    1. What is it's average speed?
      • $\overline{v} = s / t = 60m / 10s = \underline{\underline{6 m/s}} $
    2. Which Position $s$ does the Car have compared to the origin?
      • $s_T = s - s_U = 60m - 10m = \underline{\underline{50m}}$

  7. What is the velocity $v$ of a Car, that is already driving at $v_A=10m/s$ and accelerates at $0.1m/s^2$ for $10$ seconds?

    1. What is it's endvelocity $v_E$?
      • $v_E=v_A+a*t=10m/s+0.1m/s^2*10=\underline{\underline{11m/s}}$

  8. A car has a startvelocity $v_A = 6m/s$ and travels $40m$ within the first $5s$.

    1. What is the acceleration?
      • $s = v_A*t + 0.5at^2$
      • $40 = 6*5 + 0.5a*(5^2)$
      • $40 = 30 + 0.5a*25$
      • $40 = 30 + 12.5a$
      • $10 = 12.5a$
      • $a = 0.8m/s^2$