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A race car, starting from rest, accelerates at 20.0 m/s² for 5.00 seconds. Then it decelerates at -15.00 m/s² for another 5.00 seconds. What is the total distance traveled by the car in that time?

Answer :

The total distance traveled by the car during the time, given that it accelerated from rest is 562.5 m

How to determine the total distance traveled?

First, we shall obtain the distance traveled in the first 5 s. Details below:

  • Initial velocity (u) = 0 m/s
  • Acceleration(a) = 20 m/s²
  • Time (t) = 2.5 seconds
  • Distance traveled (s₁) =?

s₁ = ut + ½at²

= (0 × 10) + (½ × 20 × 5²)

= 0 + (½ × 20 × 25)

= 0 + 250

= 250 m

Next, we shall obtain the final velocity during the first 5 s. This is shown below:

  • Initial velocity (u) = 0 m/s
  • Acceleration (a) = 20 m/s²
  • Time (t) = 5 s
  • Final velocity (v) =?

v = u + at

= 0 + (20 × 5)

= 100 m/s

Next, we shall obtain the distance during the deceleration. Details below:

  • Initial velocity (u) = 100 m/s
  • Deceleration(a) = -15 m/s²
  • Time (t) = 5 s
  • Distance traveled (s₂) =?

s₂ = ut + ½at²

= (100 × 5) + (½ × -15 × 5²)

= 500 + (½ × -15 × 25)

= 500 - 187.5

= 312.5 m

Finally, we shall obtain the total distance traveled by the car. This is shown below:

  • Distance traveled during the acceleration (s₁) = 250 m
  • Distance traveled during the deceleration(s₂) = 312.5
  • Total distance =?

Total distance = s₁ + s₂

= 250 + 312.5

= 562.5 m

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