Answer:
Vf₁ = 30 m/s
s₂ = 90 m
car wins the race.
Explanation:
To find the speed of car after 5 s, we use 1st equation of motion:
Vf₁ = Vi₁ + a₁t₁
where,
Vf₁ = Final Speed of Car = ?
Vi₁ = Initial Speed of Car = 0 m/s
a₁ = acceleration of car = 5 m/s²
t₁ = time = 5 s
Therefore,
Vf₁ = 0 m/s + (5 m/s²)(5 s)
<u>Vf₁ = 25 m/s</u>
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To find the distance of motorcycle after 6 s, we use 2nd equation of motion:
s₂ = Vi₂ t₂ + (1/2)a₂t₂²
where,
s₂ = distance covered by the motorcycle = ?
Vi₁ = Initial Speed of motorcycle = 0 m/s
a₂ = acceleration of motorcycle = 8 m/s²
t₂ = time = 6 s
Therefore,
s₂ = (0 m/s)(6 s) + (1/2)(5 m/s²)(6 s)²
<u>s₂ = 90 m</u>
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We can use 2nd equation of motion to find time taken by each car and motorcycle to reach the finish point:
For Car:
s₁ = Vi₁ t₁ + (1/2)a₁t₁²
where,
s₁ = 200 m - 50 m = 150 m (since, car starts 50 m ahead)
Therefore.
150 m = (0 m/s)(t₁) + (1/2)(5 m/s²)t₁²
t₁ = √60 s²
t₁ = 7.74 s
For Motorcycle:
s₂ = Vi₂ t₂ + (1/2)a₂t₂²
where,
s₁ = 200 m
Therefore.
200 m = (0 m/s)(t₂) + (1/2)(5 m/s²)t₂²
t₂ = √80 s²
t₂ = 8.94 s
Since, the car takes less time to reach finish line.
Therefore, car wins the race.
