Answer :
An automobile traveling in the left lane at 60.1 km/h to overtake (become even with) another car that is traveling in the right lane at 38.1 km/h, when the cars' front bumpers are initially 105.2 m apart and the time taken is t = 17.21 seconds.
To find the time, the given values are,
Distance in,
Left lane = 60.1 km/hr
Right lane = 38.1 km/hr
Initial length d₀ = 105.2 m
What is Distance?
The distance covered can be derived using the equation of motion with no acceleration.
distance d = speed v × time t
d = vt
For the first automobile,
v = 60.1 km/h
d₁ = 60.1
For the second automobile,
v = 38.1 km/h
Initial distance d = 105.2 m = 0.1052 km
d = vt + d₀.
d₂ = 38.1 t + 0.1052
For them to meet/overtake each other,
Their distance at that time must be equal.
d₁ = d₂
60.1 t = 38.1 t + 0.1052
60.1 t - 38.1 t = 0.1052
22 t = 0.1052
t = 0.1052 / 22 hr
Converting to seconds
t = 0.1052 / 22 × 3600s
t = 17.21 seconds.
The time taken for an automobile to travel is 17.21 seconds.
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