Answer:
s = 83.85 km
Step-by-step explanation:
First we calculate the distance covered by car, while traveling at constant speed:
s₁ = v₁t₁
where,
s₁ = distance covered at constant speed = ?
v₁ = constant speed = 23 m/s
t₁ = time of travel at constant speed = 1 hr = 3600 s
Therefore,
s₁ = (23 m/s)(3600 s)
s₁ = 82800 m = 82.8 km
Now, we calculate the distance travelled in accelerated motion. First we use 1st equation of motion to find acceleration:
Vf = Vi + at₂
where,
Vf = Final velocity = 40 m/s
Vi = Initial Velocity = 30 m/s
a = acceleration = ?
t₂ = time = 30 s
Therefore,
40 m/s = 30 m/s + a(30 s)
a = 10 m/s/30 s
a = 0.33 m/s²
Now, we use 2nd equation of motion for distance:
s₂ = Vi t₂ + (1/2)at₂²
s₂ = (30 m/s)(30 s) + (1/2)(0.33 m/s²)(30 s)²
s₂ = 900 m + 150 m
s₂ = 1050 m = 1.05 km
So, the total distance covered was:
s = s₁ + s₂
s = 82.8 km + 1.05 km
s = 83.85 km