Question

A car initially traveling at 3.2 m/s accelerated uniformly to a speed of 14.9 m/s over a distance of 60 meters. How much time does it take for the car to reach 9 m/s? Report your answer to 1 decimal place. Do not type in the unit or the computer will mark your answer incorrect.

Answer 1

Given

Initial velocity, u=3.2 m/s

Final speed , v=14.9 m/s

Distance travelled, s=60 m

To find

Time taken to reach 9 m/s

Step-by-step explanation

By equation of kinematics,

`\begin{gathered} v^2=u^2+2as \\ \Rightarrow14.9^2=3.2^2+2a*60 \\ \Rightarrow222.01=10.24+12a \\ \Rightarrow a=17.65\text{ m/s}^2 \end{gathered}`

Let the time taken to reach 9 m/s be t

Thus

taking v=9 m/s here we have

`\begin{gathered} v=u+at \\ \Rightarrow9=3.2+17.65t \\ \Rightarrow t=0.3\text{ s} \end{gathered}`

Conclusion

The required time is 0.3 s