QuestionA vehicle goes 25 mph and speeds up by 3 mph each second. Is it legal after 7 seconds?

Studdy Solution

STEP 1

Assumptions1. The initial speed of the vehicle is25 miles per hour. The speed of the vehicle increases by3 miles per hour every second3. We want to find out the speed of the vehicle after7 seconds4. The legal speed limit is not specified, so we will assume a common highway speed limit of70 miles per hour

STEP 2

First, we need to convert the initial speed and the speed increase from miles per hour to miles per second, since the speed increase is given in seconds. We know that1 hour is equal to3600 seconds.
$Initial\, speed\, (miles/second) = Initial\, speed\, (miles/hour) /3600$ $Speed\, increase\, (miles/second) = Speed\, increase\, (miles/hour) /3600$

STEP 3

Now, plug in the given values for the initial speed and speed increase to calculate these in miles per second.
$Initial\, speed\, (miles/second) =25 /3600$ $Speed\, increase\, (miles/second) =3 /3600$

STEP 4

Calculate the initial speed and speed increase in miles per second.
$Initial\, speed\, (miles/second) =25 /3600 =0.00694\, miles/second$ $Speed\, increase\, (miles/second) =3 /3600 =0.00083\, miles/second$

STEP 5

Now that we have the initial speed and speed increase in miles per second, we can calculate the speed of the vehicle after7 seconds. This can be done by multiplying the speed increase by the time and adding this to the initial speed.
$Speed\, after\,7\, seconds = Initial\, speed + (Speed\, increase \\times Time)$

STEP 6

Plug in the values for the initial speed, speed increase, and time to calculate the speed after seconds.
$Speed\, after\,\, seconds =0.00694 + (0.00083 \\times)$

STEP 7

Calculate the speed after7 seconds in miles per second.
$Speed\, after\,7\, seconds =0.00694 + (0.00083 \\times7) =0.01275\, miles/second$

STEP 8

To compare this with the legal speed limit, we need to convert the speed after7 seconds back to miles per hour. We can do this by multiplying the speed in miles per second by3600.
$Speed\, after\,7\, seconds\, (miles/hour) = Speed\, after\,7\, seconds\, (miles/second) \\times3600$

STEP 9

Plug in the value for the speed after7 seconds to calculate this in miles per hour.
$Speed\, after\,7\, seconds\, (miles/hour) =.01275 \\times360$

STEP 10

Calculate the speed after7 seconds in miles per hour.
$Speed\, after\,7\, seconds\, (miles/hour) =0.01275 \\times3600 =45.9\, miles/hour$ The vehicle is traveling at45.9 miles per hour after7 seconds. Since this is below the assumed legal speed limit of70 miles per hour, the vehicle is traveling at a legal speed.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms