Question

During an endurance race, part of a car's total distance traveled can be found by multiplying its top

speed (150 km/h) by the number of hours that it takes for the car to finish the race. The other part of
the total distance is the distance it takes for the car to get to top speed, in this case, % of a kilometer.
The car takes 0.01 hours to travel the initial % of a kilometer.
If the car reaches top speed, then drives at top speed for 3.75 hours, how far did the car travel during
the race?
1. Solve the problem above using simple arithmetic.

Answer 1

563.25 km

Explanation:

let
`d_1` be the the distance it takes for the car to get to top speed and
`d_2` be distance traveled can be found by multiplying its top speed (150 km/h) by the number of hours that it takes for the car to finish the race. The total distance d is given as:

`d=d_1+d_2`

To get
`d_1`, the car is initially at rest (i.e 0 km/h) and then it accelerates to a speed of 150 km/hr within 0.01 hrs. Let u = initial velocity = 0 km/hr, v = final velocity = 150 km/hr and the time taken (
`t_1`) = 0.01 hrs. Therefore:

`d_1=((v+u)/(2) )t=((0+150)/(2) )0.01=0.75km`

To get
`d_2` , we use the formula
`d_2` = v
`t_2`, where v =150 km / hr and
`t_2` = 3.75 hrs. Therefore:

`d_2=150*3.75=562.5km`

`d=d_1+d_2=562.5+0.75=563.25km`