Question

velocity math problems 5 pts each. use the graph to find the cyclists total average speed for their entire journey. show 11. a rocket heading up into space travels 5,000 meters in 5 seconds. find its velocity. for 12 - 14 identify the units as speed units, velocity units, or neither. (1 pt each) 12. 9.5 m/min down 13. 29 cm/hr 14. 55 cm true or false (1 pt each) 15. if you know the speed of an object, you also know the direction of movement. 16. the information needed for describing velocity is distance, time, and direction. 17. to determine the speed of an object, divide time by distance.

Explanation:

Step1: Recall average - speed formula

The formula for average speed is $v_{avg}=\frac{\text{Total Distance}}{\text{Total Time}}$.

Step2: Determine total distance and time from the graph

From the graph, the total distance $d = 8$ km and the total time $t=30$ minutes. Since $1$ km = $1000$ m and $1$ minute=$60$ s, first convert the units. $d = 8\times1000$ m and $t = 30\times60$ s.

Step3: Calculate average speed

$v_{avg}=\frac{8\times1000}{30\times60}=\frac{8000}{1800}=\frac{40}{9}\approx4.44$ m/s. In km/h, $v_{avg}=\frac{8}{\frac{30}{60}} = 16$ km/h.

for rocket velocity:

Step1: Recall velocity formula

Velocity $v=\frac{\text{Displacement}}{\text{Time}}$. Given displacement $s = 5000$ m and time $t = 5$ s.

Step2: Calculate velocity

$v=\frac{5000}{5}=1000$ m/s.

for unit - identification:

Step1: Analyze 9.5 m/min down

Since it has a direction ("down") along with a rate of change of position with respect to time, it is a velocity unit.

Step2: Analyze 29 cm/hr

It only gives a rate of change of position with respect to time without a direction, so it is a speed unit.

Step3: Analyze 55 cm

It is just a distance measurement, so it is neither a speed nor a velocity unit.

for true - false questions:

Step1: Analyze statement 15

Speed is a scalar quantity and does not include direction. So, if you know the speed of an object, you do not know the direction of movement. False.

Step2: Analyze statement 16

Velocity is a vector quantity and is described by distance, time, and direction. True.

Step3: Analyze statement 17

To determine the speed of an object, divide distance by time ($v=\frac{d}{t}$), not time by distance. False.

Answer:

The cyclist's total average speed is $16$ km/h (or $\frac{40}{9}\approx4.44$ m/s)