A car starting from rest moves with a constant acceleration of 10 mi/hr2 for 1 hour, then decelerates at a constant 5 mi/hr2 until it comes to a stop. How far has it travelled?

The total distance traveled by the car (S) = 15 mi

Explanation:

Total acceleration () = 10 mi /

Time (t) = 1 hour

Deceleration () = - 5 mi /

From law of speed we know that  V = u + 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 = t = 10 × 1 = 10 mi / h ---------(2)

The distance traveled by the car = u t + × × -------------(3)

Put all the values in equation we get = 0 + × 10 ×

                                                              = 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   = u t + × ×

⇒ = 10 × 2 - × 5 ×

⇒ = 20 - 10

⇒ = 10 mi

This is the distance traveled by the car in the next two hours.

Thus the total distance traveled by the car = +

⇒ S = 5 + 10 = 15 mi

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