Question

name _ date _ class 1 2 3 4 5 6 7 - motion and newton’s laws part 1 -calculations: speed, velocity, acceleration & force calculations 1. match the following quantities with the correct si unit. distance a. meter/second (m/s) with a given direction time b. newton (kgm/s²) speed c. meter/second squared (m/s²) velocity d. second (s) acceleration e. meter/second (m/s) force f. meter 2. a dog travels 250 meters east in 8 seconds. what is the velocity of the dog? 3. when you calculate acceleration, what does it mean if your answer is positive? what does it mean when your answer is negative? 4. a turtle swimming in a straight line toward shore has a speed of 0.53 m/s. after 4.0s, its speed is 0.75 m/s. what is the turtle’s acceleration? 5. chris is driving south down i -75. he notices a police officer and slows down from 42 m/s to 33 m/s in 7.0s. calculate his deceleration. 6. a cyclist accelerates from rest to 8 m/s in 5 seconds. what is his/her acceleration? 7. suppose you’re driving 90.0 km/hr and suddenly see red flashing lights in the rearview mirror. if it takes you 20s (0.006 hrs) to come to a stop, calculate your deceleration. 8. a pitcher accelerates a baseball with a mass of 1.5 kg at 6m/s². how much force does this take? v = \frac{d}{t} a = \frac{v_f - v_i}{t} f = ma

Explanation:

Step1: Match SI - units

Distance - f. meter
Time - d. second (s)
Speed - e. meter/second (m/s)
Velocity - a. meter/second (m/s) with a given direction
Acceleration - c. meter/second squared (m/s²)
Force - b. Newton (kgm/s²)

Step2: Calculate dog's velocity

Use the formula $V=\frac{D}{T}$. Given $D = 250$ m and $T = 8$ s, and direction is east.
$V=\frac{250}{8}=31.25$ m/s east

Step3: Interpret acceleration sign

A positive acceleration means the object is speeding up (increasing velocity). A negative acceleration (deceleration) means the object is slowing down (decreasing velocity).

Step4: Calculate turtle's acceleration

Use the formula $A=\frac{V_f - V_i}{T}$. Given $V_i=0.53$ m/s, $V_f = 0.75$ m/s and $T = 4.0$ s.
$A=\frac{0.75 - 0.53}{4}=\frac{0.22}{4}=0.055$ m/s²

Step5: Calculate Chris's deceleration

Use the formula $A=\frac{V_f - V_i}{T}$. Given $V_i = 42$ m/s, $V_f=33$ m/s and $T = 7.0$ s.
$A=\frac{33 - 42}{7}=\frac{- 9}{7}\approx - 1.29$ m/s²

Step6: Calculate cyclist's acceleration

Use the formula $A=\frac{V_f - V_i}{T}$. Given $V_i = 0$ m/s (starts from rest), $V_f = 8$ m/s and $T = 5$ s.
$A=\frac{8 - 0}{5}=\frac{8}{5}=1.6$ m/s²

Step7: Calculate driver's deceleration

First convert the initial velocity to m/s. $90.0$ km/hr=$90\times\frac{1000}{3600}=25$ m/s, $V_f = 0$ m/s, $T = 20$ s.
Use the formula $A=\frac{V_f - V_i}{T}=\frac{0 - 25}{20}=-1.25$ m/s²

Step8: Calculate force on baseball

Use the formula $F = ma$. Given $m = 1.5$ kg and $a = 6$ m/s².
$F=1.5\times6 = 9$ N

Answer:

1. Distance - f. meter; Time - d. second (s); Speed - e. meter/second (m/s); Velocity - a. meter/second (m/s) with a given direction; Acceleration - c. meter/second squared (m/s²); Force - b. Newton (kgm/s²)
2. 31.25 m/s east
3. Positive: speeding up; Negative: slowing down
4. 0.055 m/s²
5. - 1.29 m/s²
6. 1.6 m/s²
7. - 1.25 m/s²
8. 9 N