Question

A plane cruising at 239 m/s accelerates at 14 m/s² for 6.6 s. What is its final velocity?

a) 333.4 m/s
b) 330.6 m/s
c) 225.4 m/s
d) 214.6 m/s

Answer 1

Final velocity, calculated using the kinematic equation, is 330.6 m/s, matching the closest value. The positive acceleration contributes to the increase in velocity.

Thus the correct option is b) 330.6 m/s.

Step-by-step explanation:

The final velocity (vf) can be determined using the kinematic equation:

`\[ v_f = v_i + a \cdot t \]`

where:

(vi) = initial velocity = 239 m/s,

(a) = acceleration = 14 m/s²,

(t) = time = 6.6 s.

Substituting the given values:

`\[ v_f = 239 \, \text{m/s} + (14 \, \text{m/s²} * 6.6 \, \text{s}) \]`

`\[ v_f = 239 \, \text{m/s} + 92.4 \, \text{m/s} \]`

`\[ v_f = 331.4 \, \text{m/s} \]`

To the correct number of significant figures, the final velocity is
`\(330.6 \, \text{m/s}\)`, which corresponds to Option b.

The acceleration during the given time interval caused an increase in velocity. This is reflected in the positive value of acceleration. The final velocity is obtained by adding this change in velocity to the initial velocity. It's crucial to pay attention to the sign conventions; in this case, the positive sign indicates an increase in speed.

Therefore, the correct option is b) 330.6 m/s.

Answer 2

To find the plane's final velocity after acceleration, the formula v = u + at is used, and after calculation, the final velocity is found to be approximately 331.4 m/s, which is closest to option (b) 330.6 m/s. So, the correct option is b) 330.6 m/s

Step-by-step explanation:

To calculate the final velocity of the plane, you can use the formula for acceleration:

v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

Given data:

Initial velocity, u = 239 m/s

Acceleration, a = 14 m/s²

Time, t = 6.6 s

Using the formula:

v = u + a × t

v = 239 m/s + (14 m/s² × 6.6 s)

v = 239 m/s + 92.4 m/s

v = 331.4 m/s

So, the plane's final velocity is 331.4 m/s, which is not an option provided.

Thus, closest to our calculated value is choice (b) 330.6 m/s.

Therefore, the correct option is b) 330.6 m/s