Question

Simpson drives his car with an average velocity of 26 m/s toward the east.a. How long will it take him to drive 860 km on a perfectly straight highway?b. How much time would Simpson save by increasing his average velocity to 28 m/s east?

Answer 1

`\begin{gathered} a.\text{ }33,076.92\text{ s or }551.28\text{ mins or }9.19\text{ hrs} \\ \\ b.\text{ }2,362.63\text{ s or }39.38\text{ mins or }0.66\text{ hr} \end{gathered}`

Step-by-step explanation

a. To find how long it will take him to drive 860 km on a perfectly straight highway, we have to apply the formula for velocity:

`\begin{gathered} v=(d)/(t) \\ \\ t=(d)/(v) \end{gathered}`

where d = displacement; t = time taken

But first, we have to convert the displacement to meters:

`860\text{ km }=860*1000\text{ m }=860,000\text{ m}`

Now, find the time it will take:

`\begin{gathered} t=(860,000)/(26) \\ \\ t=33,076.92\text{ s }=551.28\text{ mins }=9.19\text{ hrs} \end{gathered}`

That is the answer.

b. To find the time that Simpson would save, first, find the time that it will take to travel 860 km (860,000 m) at a velocity of 28 m/s:

`\begin{gathered} t=(860,000)/(28) \\ \\ t=30,714.29\text{ s} \end{gathered}`

Now, find the difference in the time for both velocities:

`\begin{gathered} \Delta t=33,076.92-30,714.29 \\ \\ \Delta t=2,362.63\text{ s or }39.38\text{ mins or }0.66\text{ hr} \end{gathered}`

That is the answer.