An object is moving east, and its velocity changes from 65 m/s to 25 m/s in 10 seconds. Which describes the acceleration?

negative acceleration of 4 m/s2
positive acceleration of 4 m/s2
positive acceleration of 9 m/s2
negative acceleration of 9 m/s2

1 answer

To determine the acceleration, we can use the formula for acceleration:

\[ a = \frac{{v_f - v_i}}{{t}} \]

where:

  • \( v_f \) is the final velocity,
  • \( v_i \) is the initial velocity,
  • \( t \) is the time.

In this case:

  • \( v_f = 25 , \text{m/s} \)
  • \( v_i = 65 , \text{m/s} \)
  • \( t = 10 , \text{s} \)

Now, substituting the values into the formula:

\[ a = \frac{{25 , \text{m/s} - 65 , \text{m/s}}}{{10 , \text{s}}} \]

\[ a = \frac{{-40 , \text{m/s}}}{{10 , \text{s}}} \]

\[ a = -4 , \text{m/s}^2 \]

Since the acceleration is negative, this indicates that the object is decelerating (slowing down).

Thus, the correct description of the acceleration is negative acceleration of 4 m/s².