A car travels 23.0 m/s for 1.0 hours and then accelerates for 30.0 seconds to reach 40.0 m/s.  What was the total distance traveled by this car

s = 83.85 km

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

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