Question

llowing questions. show your work and include correct units.
table of equations
ity: ( v_f = v_i + (a cdot t) )
time: ( t = d / v )
ity: ( v_f = v_i - (a cdot t) )
centripetal acceleration: ( a = v^2 / r )
( d = v cdot t )
linear acceleration: ( a = (v_f - v_i) / t )
gravity (earth): ( 9.8 , \text{m/s}^2 )

a ball is dropped from the top of a building. after 2 seconds, its velocity is measured to be 19.6 m/s. what is the acceleration of the ball?
what are you solving for? \t equation:
acceleration \t ( v = v_0 + (a cdot t) )
show work and answer with the correct units:
( a = 9.8 , \text{m/s}^2 )

1. a runner sprints 400 meters east in 50 seconds, then jogs another 600 meters east in 2 minutes. what is their average velocity for the entire run?

what are you solving for? \t equation:
average velocity \t ( v = d / t )
show work and answer with the correct units:

1. a plane flies at 500 km/h for 15 minutes. how far does it travel?

what are you solving for? \t equation:
\t
show work and answer with the correct units:

1. a ball is launched upward and is in the air for a total of 4 seconds before returning to its starting hei what was the initial velocity? (remember gravity is an acceleration value!)

what are you solving for? \t equation:
\t
show work and answer with the correct units:

Explanation:

Question 11 (Ball Dropped from Building)

Step1: Identify known values

Initial velocity \( v_i = 0 \, \text{m/s} \) (dropped), final velocity \( v_f = 19.6 \, \text{m/s} \), time \( t = 2 \, \text{s} \). We use the linear acceleration formula \( a=\frac{v_f - v_i}{t} \).

Step2: Substitute values into formula

\( a=\frac{19.6 - 0}{2} \)

Step3: Calculate acceleration

\( a = 9.8 \, \text{m/s}^2 \)

Step1: Find total distance and total time

Total distance \( d = 400 + 600 = 1000 \, \text{m} \). Total time \( t = 50 \, \text{s}+2\times60 = 170 \, \text{s} \). Use \( v=\frac{d}{t} \).

Step2: Substitute values

\( v=\frac{1000}{170}\approx5.88 \, \text{m/s} \) (east direction, but magnitude is \( \approx5.88 \, \text{m/s} \))

Step1: Convert time to hours

\( 15 \, \text{minutes}=\frac{15}{60}=0.25 \, \text{h} \). Use \( d = v\times t \), where \( v = 500 \, \text{km/h} \), \( t = 0.25 \, \text{h} \).

Step2: Calculate distance

\( d = 500\times0.25 = 125 \, \text{km} \)

Answer:

The acceleration of the ball is \( 9.8 \, \text{m/s}^2 \)

Question 12 (Runner's Average Velocity)