Question

An object has an average acceleration of +5.27 m/s² for 0.300 s. At the end of this time, the object's velocity is +9.88 m/s. What was the object's initial velocity?

a) +8.19 m/s
b) +11.43 m/s
c) +7.79 m/s
d) +6.72 m/s

Answer 1

To find the initial velocity, we use the kinematic equation vf = vo + a*t. Given the final velocity of +9.88 m/s, the average acceleration of +5.27 m/s², and the time interval of 0.300 s, the initial velocity is calculated to be approximately +8.30 m/s, which matches closest with option a: +8.19 m/s.

Step-by-step explanation:

The question is asking to calculate the object's initial velocity given the final velocity, the average acceleration, and the time period. We can use the kinematic equation that relates these quantities:

vf = vo + a*t

Where:

• vf is the final velocity
• vo is the initial velocity
• a is the acceleration
• t is the time

We are given that vf = +9.88 m/s, a = +5.27 m/s2, and t = 0.300 s. Plugging these values into the equation gives:

9.88 m/s = vo + (5.27 m/s2 * 0.300 s)

9.88 m/s = vo + 1.581 m/s

Therefore, the initial velocity vo can be found by subtracting 1.581 m/s from 9.88 m/s:

vo = 9.88 m/s - 1.581 m/s

vo = +8.299 m/s

When rounding to the hundredths place, the initial velocity is approximately +8.30 m/s. Looking at the given options, the one closest to our calculated value is +8.19 m/s (Option a).

Thus, the correct answer is Option a: +8.19 m/s.