Question

A car moves in a straight line at 22.0 m/s for 10.0miles, then at 30.0 m/s for another 10.0miles. Calculate the car’s average speed in m/s

Answer 1

Answer: 25.38 m/s

Step-by-step explanation:

We have a straight line where the car travels a total distance
`D`, which is divided into two segments
`d=10 miles`:

`D=d+d=2d` (1)

Where
`d=10mi (1609.34 m)/(1 mi)=16093.4 m`

On the other hand, we know speed is defined as:

`S=(d)/(t)` (2)

Where
`t` is the time, which can be isolated from (2):

`t=(d)/(S)` (3)

Now, for the first segment
`d=16093.4 m` the car has a speed
`S_(1)=22m/s`, using equation (3):

`t_(1)=(d)/(S_(1))` (4)

`t_(1)=(16093.4 m)/(22m/s)` (5)

`t_(1)=731.518 s` (6) This is the time it takes to travel the first segment

For the second segment
`d=16093.4 m` the car has a speed
`S_(1)=30m/s`, hence:

`t_(2)=(d)/(S_(2))` (7)

`t_(2)=(16093.4 m)/(30m/s)` (8)

`t_(2)=536.44 s` (9) This is the time it takes to travel the secons segment

Having these values we can calculate the car's average speed
`S_(ave)`:

`S_(ave)=(d + d)/(t_(1) + t_(2))=(2d)/(t_(1) + t_(2))` (10)

`S_(ave)=(2(16093.4 m))/(731.518 s +536.44 s)` (11)

Finally:

`S_(ave)=25.38 m/s`