Question

Assuming a constant deceleration of 4.7 m/s² from a speed of 17 m/s, if the speed is doubled to 34 m/s, does the time required to come to a stop increase by a factor of two or four?

Options:
A) Increase by a factor of 2
B) Increase by a factor of 4
C) Increase by a factor of 3
D) Decrease by a factor of 2

Answer 1

The correct answer is option A) Increase by a factor of 2. The time required to come to a stop increases by a factor of 2 when the speed is doubled.

Step-by-step explanation:

The correct answer is option A) Increase by a factor of 2.

When the speed is doubled to 34 m/s, the time required to come to a stop increases by a factor of 2. Here's the step-by-step explanation:

1. First, we need to calculate the time required to come to a stop from a speed of 17 m/s using the constant deceleration of 4.7 m/s².
2. Using the formula: Final velocity = Initial velocity + (acceleration * time). Rearranging the formula to solve for time: time = (Final velocity - Initial velocity) / acceleration.
3. Substituting the given values: time = (0 - 17) / -4.7 = 3.62 seconds.
4. Next, we double the speed to 34 m/s.
5. To find the new time required to come to a stop, we use the same formula: time = (Final velocity - Initial velocity) / acceleration.
6. Substituting the values: time = (0 - 34) / -4.7 = 7.23 seconds.

Therefore, the time required to come to a stop increases by a factor of 2 when the speed is doubled.