Question

objectives: analyze and explain velocity vs. time graphs.
vocabulary: acceleration
practice:

1. list the different ways an object can accelerate.
2. analyze the motion of an object that has an acceleration of 0 m/s²
3. by the time an airplane reaches the end of a runway, it has reached a speed of 80 m/s in 20 s. what is its acceleration?
4. a puppy is running with a speed of 11.2 m/s towards its owner when it gets distracted by a squirrel and stops running. if it halted its run in 2 s, what was the acceleration of the puppy?
5. explain what the slopes on a distance vs. time graph and on a velocity vs. time graph tell you.
6. a ball is dropped from a cliff and has an acceleration of 9.8 m/s². how long will it take the ball to reach a speed of 24.5 m/s?
7. indicate what kind of acceleration is shown in the following graphs.

Explanation:

12.

Step1: Recall acceleration formula

The formula for acceleration is $a=\frac{v - u}{t}$, where $v$ is final - velocity, $u$ is initial - velocity, and $t$ is time. The airplane starts from rest, so $u = 0\ m/s$, $v=80\ m/s$, and $t = 20\ s$.

Step2: Substitute values into formula

$a=\frac{80 - 0}{20}$
$a = 4\ m/s^{2}$

Step1: Identify initial and final velocities and time

The puppy's initial velocity $u = 11.2\ m/s$, final velocity $v = 0\ m/s$ (it stops), and time $t = 2\ s$.

Step2: Use acceleration formula

$a=\frac{v - u}{t}=\frac{0 - 11.2}{2}$
$a=- 5.6\ m/s^{2}$

On a distance - vs - time graph, the slope represents the speed of the object. A steeper slope means a higher speed. On a velocity - vs - time graph, the slope represents the acceleration of the object. A positive slope means positive acceleration, a negative slope means negative acceleration (deceleration), and a zero slope means zero acceleration (constant velocity).

Answer:

$4\ m/s^{2}$

13.