Answer :
Answer:
The total distance traveled by the car (S) = 15 mi
Explanation:
Total acceleration ([tex]a_{1}[/tex]) = 10 mi / [tex]h^{2}[/tex]
Time (t) = 1 hour
Deceleration ([tex]a_{2}[/tex]) = - 5 mi / [tex]h^{2}[/tex]
From law of speed we know that V = u + [tex]a_{1}[/tex] t -----------(1)
Where V = Final speed
u = initial speed and t = time period
Car starts from rest so initial speed is zero so u = 0
Then equation 1 becomes V = [tex]a_{1}[/tex] t = 10 × 1 = 10 mi / h ---------(2)
The distance traveled by the car [tex]S_{1}[/tex] = u t + [tex]\frac{1}{2}[/tex] × [tex]a_{1}[/tex] × [tex]t^{2}[/tex] -------------(3)
Put all the values in equation we get [tex]S_{1}[/tex] = 0 + [tex]\frac{1}{2}[/tex] × 10 × [tex]1^{2}[/tex]
[tex]S_{1}[/tex] = 5 mi ---------------(4)
This is the distance traveled by the car in 1 hour.
In second case when car starts decelerates the equation of motion becomes
⇒ V = u - a t -----------(5)
final speed in this case = 0 and initial speed (u) = 10 mi / h
⇒ 0 = 10 - 5 t
⇒ 5 t = 10
⇒ t = 2 hours
Distance traveled by the car in to hours [tex]S_{2}[/tex] = u t + [tex]\frac{1}{2}[/tex] × [tex]a_{2}[/tex] × [tex]t^{2}[/tex]
⇒ [tex]S_{2}[/tex] = 10 × 2 - [tex]\frac{1}{2}[/tex] × 5 × [tex]2^{2}[/tex]
⇒ [tex]S_{2}[/tex] = 20 - 10
⇒ [tex]S_{2}[/tex] = 10 mi
This is the distance traveled by the car in the next two hours.
Thus the total distance traveled by the car = [tex]S_{1}[/tex] + [tex]S_{2}[/tex]
⇒ S = 5 + 10 = 15 mi