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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