Respuesta :
Given data:
* The mass of the car is m = 1250 kg.
* The initial velocity of the car is u = 0 m/s.
* The final velocity of the car is,
[tex]\begin{gathered} v=95\text{ km/h} \\ v=95\times\frac{1000}{60\times60}\text{ m/s} \\ v=26.39\text{ m/s} \end{gathered}[/tex]* The time taken by the car to increase its velocity is t = 8.5 s.
Solution:
(a). The acceleration of the car is,
[tex]a=\frac{v-u}{t}[/tex]Substituting the known values,
[tex]\begin{gathered} a=\frac{26.39-0}{8.5} \\ a=3.1ms^{-2} \end{gathered}[/tex]Thus, the acceleration of the car is 3.1 meters per second.
(b). By the kinematics equation, the displacement of the car is,
[tex]S=ut+\frac{1}{2^{}}at^2[/tex]Substituting the known values,
[tex]\begin{gathered} S=0+\frac{1}{2}\times3.1\times8.5^2 \\ S=112\text{ m} \end{gathered}[/tex]Thus, the displacement of the car is 112 meters.
(c). The work done by the car in 8.5 seconds is,
[tex]W=\frac{1}{2}mv^2-\frac{1}{2}mu^2[/tex]Substituting the known values,
[tex]\begin{gathered} W=\frac{1}{2}\times1250\times26.39^2 \\ W=435270\text{ J} \end{gathered}[/tex]Thus, the work done by the car is 435270 J.
(d). The average power required for the motion is,
[tex]\begin{gathered} P=\frac{W}{t} \\ P=\frac{435270}{8.5} \\ P=51208.2\text{ watts} \end{gathered}[/tex]Thus, the power required for the given motion is approximately 51208 watts.
