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How long would the car in sample problem c take to come to a stop from its initial velocity of 20.0 m/s to the west? How far would the car move before stopping? Assume a constant acceleration.

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Final answer:

Assuming a hypothetical constant deceleration of -5.0 m/s², a car initially traveling at 20.0 m/s would take 4.0 seconds to stop, and the car would travel a distance of 40.0 meters before coming to a complete halt.

Step-by-step explanation:

To answer the student's question about how long it would take for a car to come to a stop from its initial velocity of 20.0 m/s to the west and how far the car would move before stopping, we would need the value of constant acceleration; however, since it's not provided, I'll demonstrate the process with a hypothetical acceleration value.

Calculating the Stopping Time

If we assume an acceleration of -5.0 m/s2 (negative because the car is decelerating), we can use the formula:

final velocity (v) = initial velocity (u) + acceleration (a) × time (t)

Here, we want to find the time taken (t) for the car to come to a stop (final velocity = 0).

0 = 20.0 m/s - (5.0 m/s2 × t)

t = (20.0 m/s) / (5.0 m/s2)

t = 4.0 seconds

Calculating the Stopping Distance

We can then calculate the stopping distance using the formula:

distance (s) = (initial velocity (u) × time (t)) + (0.5 × acceleration (a) × time (t)2)

s = (20.0 m/s × 4.0 s) + (0.5 × -5.0 m/s2 × (4.0 s)2)

s = 40.0 m

User Jack Bonneman
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