**42. A train has a length of 92 m and starts from rest with a constant acceleration at time

t = 0 s. At this instant, a car just reaches the end of the train. The car is moving with a constant velocity. At a time t = 14 s, the car just reaches the front of the train. Ultimately, however, the train pulls ahead of the car, and at time t = 28 s, the car is again at the rear of the train. Find the magnitudes of (a) the car’s velocity and (b) the train’s acceleration.

We know , and , and , and

at t₁ = 14 s, L = 92 m and at t₂ = 28 s, L = 0 m.

At time t₁, the distance the car travels is the same as the distance the train travels plus the length of the train. At time t₂, the distance the car travels is the same as the distance the train travels. Basic equation is

For car this becomes

And for train

So for t₁

So we have

At t₂

Which gives us

Solve this equation for

Plug this into previous equation

Now solve for

Now plug in to find

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This page last updated on January 11, 2020