# A car moving with constant acceleration covered the distance between two points 52.4 m apart in 5.96 s. Its speed as it passes the second point was 14.6 m/s. (a) At what prior distance from the first point was the car at rest?

The car was at rest

Here, the idea is that the car will accelerate steadily once it gets going.

This implies that you can write using the acceleration and the speed at which it passes the first point.

To begin with, you are aware of

Given that you are aware of the car's speed at the second point, you can write

Re-enter this into the equation above to obtain

Enter your values to get; for simplicity, I'll omit the units.

This will ultimately result in you

When the vehicle crosses the first point, its speed will be

As an alternative, you can first determine how long it took the vehicle to arrive at the starting point.

Before reaching the first position, the distance it traveled was

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To find the initial velocity of the car, use the equation: (v_i = v_f - at). Rearrange the equation to solve for (v_i). Then, use the equation (s = v_i t + \frac{1}{2}at^2) to find the initial position of the car.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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