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Lillian has had enough of Tiffany's antics and runs over to Tiffany's table. With an initial speed of 2m/s2\,\text{m/s}, Lillian accelerates at a rate of 18m/s218\,\text{m/s}^2 for 1.51.5 seconds, what is her final speed?\newlineA. 29m/s29\,\text{m/s}\newlineB. 35m/s35\,\text{m/s}\newlineC. 19m/s19\,\text{m/s}\newlineD. 23m/s23\,\text{m/s}

Full solution

Q. Lillian has had enough of Tiffany's antics and runs over to Tiffany's table. With an initial speed of 2m/s2\,\text{m/s}, Lillian accelerates at a rate of 18m/s218\,\text{m/s}^2 for 1.51.5 seconds, what is her final speed?\newlineA. 29m/s29\,\text{m/s}\newlineB. 35m/s35\,\text{m/s}\newlineC. 19m/s19\,\text{m/s}\newlineD. 23m/s23\,\text{m/s}
  1. Identify Given Values: Identify the given values and the formula to use.\newlineGiven values:\newlineInitial speed uu = 22 m/s\newlineAcceleration aa = 1818 m/s2^2\newlineTime tt = 1.51.5 s\newlineWe will use the formula for final velocity vv in uniformly accelerated motion: v=u+atv = u + at
  2. Substitute Values into Formula: Substitute the given values into the formula. \newlinev=u+atv = u + at\newlinev=2m/s+(18m/s2×1.5s)v = 2 \, \text{m/s} + (18 \, \text{m/s}^2 \times 1.5 \, \text{s})
  3. Perform Multiplication: Perform the multiplication to find the change in speed.\newlineChange in speed = 18m/s2×1.5s18 \, \text{m/s}^2 \times 1.5 \, \text{s}\newlineChange in speed = 27m/s27 \, \text{m/s}
  4. Find Final Speed: Add the change in speed to the initial speed to find the final speed.\newlinev=2m/s+27m/sv = 2 \, \text{m/s} + 27 \, \text{m/s}\newlinev=29m/sv = 29 \, \text{m/s}

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