Given that the initial speed, u = 0 m/s , final speed, v = 82.7 m/s and the time is, t = 60 s.
(a) To find acceleration.
Formula to find acceleration is
[tex]a=\frac{v-u}{t}[/tex]Substituting the values in the above equation, we get
[tex]\begin{gathered} a=\frac{82.7-0}{60} \\ =1.38m/s^2 \end{gathered}[/tex]Thus, the acceleration is 1.38 m/s^2.
(b) To find displacement.
The formula to find displacement is
[tex]s=ut+\frac{1}{2}at^2[/tex]Substituting the values in the above equation, we get
[tex]\begin{gathered} s=0\times60+\frac{1}{2}\times1.38\times(60)^2 \\ =2484\text{ m} \end{gathered}[/tex](c) To find final speed, v' when time, t'= 80 s
Formula to find final velocity,
[tex]v^{\prime}=u+at[/tex]Substituting the values in the above equation, we get
[tex]\begin{gathered} v^{\prime}=0+1.38\times80 \\ =110.4\text{ m/s} \end{gathered}[/tex]Thus, the final speed is 110.4 m/s for the first 80 s.
(d) The speed of the car is v''=50 m/s and acceleration, a'=60.2 m/s^2
To find the distance, s'.
The formula to find the distance is
[tex]v^{\doubleprime}^2=u^2+2a^{\prime}s^{\prime}[/tex]Substituting the values, we get distance as
[tex]\begin{gathered} s^{\prime}=\frac{(50)^2-0^2}{2\times60.2} \\ =20.76\text{ m} \end{gathered}[/tex]Thus, the distance is 20.76 m.
