# Units of measurement

1) A sphere has a radius 1.500m Find its volume in cm^3. Find its suface area in m^2 and in mm^2?

2) A truncated right circular cone has dimensions:

upper base diameter =1.50cm

lower base diameter = 4.00cm

height = 6.00cm

Find its volume in cm^3, m^3, mm^3

3) a person walks 5km in 1,5hr. What is the speed in mi/hr, m/s, and ft/s?

4) A car can accelerate from rest to 60 mi/hr in 7 s. Express this acceleration in the following units(assume constant acceleration)

ft/s^2

km/hr/s

m/s^2

5)A turntable accelerates from rest to 33 rpm in 0.6s. Express this acceleration in rev/s^2 and rad/s^2.

6)A spbway train starts from rest at a station, accelerates uniformly at a rate of 2.0 m/s^2 for 15 s, cruises at constant speed fro 30 s, and then decelerates uniformly coming to rest at the next station after a total trip time of 54 s. How far apart are the stations? Express your answers in m, km and miles.

7)An electrically powered grindstone wheel rotates at 2,000 rpm for 50 s and the power is then switched off. The wheel comes to rest 40.0 s later. Calculate: The angular deceleration in rad/s ^2 and rev/min/s.

Determine the total angular distance traveled over the 90 s time interval, expressed in both radians and revolutions?

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

1) A sphere has a radius 1.500m Find its volume in cm^3. Find its surface area in m^2 and in mm^2?

r= 1.5 metres

= 150 cm

= 1500 mm

Volume=(4/3)pi r 3= 14137167 cm3

Surface area=4pi r 2= 28.2743 m2

= 28274333.88 mm2

2) A truncated right circular cone has dimensions:

upper base diameter =1.50cm

lower base diameter = 4.00cm

height = 6.00cm

Find its volume in cm^3, m^3, mm^3

To find the volume of the truncated cone

Volume=(1/3)pi r1 2 (h1+h2)-(1/3)pi r2 2 h2=

r1= lower base radius 2 cm

or 0.02 m

or 20 mm

r2= upper base radius 0.75 cm

or 0.0075 m

or 7.5 mm

h1= height of truncated cone 6 cm

or 0.06 m

or 60 mm

h2= height by which the cone has been truncated

h2/(h1+h2)=r2/r1

or h2/(6+h2)=0.75/2= 0.375

or h2= 3.6 cm

or 0.036 m

or 36 mm

Putting these values into the equation

Volume= 38.09181092 cm3

0.000038092 m3

38091.81 mm2

Velocity-acceleration

3) a person walks 5km in 1.5hr. What is the speed in mi/hr, m/s, and ft/s?

1 Km= 1000 metres

1 mile= 1760 yards

= 5280 feet

= 1609.34 metres

1 Km= 0.6214 miles

= 3281 feet

Speed=Distance/time=

Distance= 5 Km Time= 1.5 hrs = 5400 seconds

= 3.107 miles

= 16405 feet

Speed= 2.07 mi/hr

= 0.93 m/s

= 3.04 ft/s

4) A car can accelerate from rest to 60 mi/hr in 7 s. Express this acceleration in the following units(assume constant acceleration)

ft/s^2

km/hr/s

m/s^2

acceleration= change in velocity/change in time

change in velocity= 60-0= 60 mi/hr

= 96.56 Km/hr 1 mile= 1.6093 Km

= 26.82 m/s 1 mile= 1609.34 m 1 hr= 3600 s

= 88 ft/s 1 mile= 5280 ft

change in time= 7 s

acceleration= 12.57 ft/s2

= 13.79 Km/hr/s

= 3.83 m/s2

5)A turntable accelerates from rest to 33 rpm in 0.6s. Express this acceleration in rev/s^2 and rad/s^2.

1 rpm= 2pi radians

= 6.283 radians

change in angular velocity ,w = 33 revolutions

= 207.339 radians

change in time= 0.6 s

acceleration= 55.00 rev/s2

= 345.57 rad/s2

6)A subway train starts from rest at a station, accelerates uniformly at a rate of 2.0 m/s^2 for 15 s,

cruises at constant speed from 30 s, and then decelerates uniformly coming to rest

at the next station after a total trip time of 54 s. How far apart are the stations? Express your answers in m, km and mi.

s= ut+ 1/2 a t 2

s= distance travelled

u= initial velocity

t= time

a= acceleration

There are three phases

1)When the train is accelerating

u= 0

a= 2 m/s2

t= 15 s

s= ut+ 1/2 a t 2= 225 metres

2)When the train is moving at constant speed for 30 seconds

After the train has accelerated for 15 seconds the velocity is

v=u+at= 30 m/s

s=vt= 900 metres

3)When the train is decelerating

u= 30 m/s

v= 0 m/s

t= 9 s =54-(15+30); 15 seconds for part 1 and 30 seconds for part 2

v=u+at

a=(v-u)/t= -3.33 m/s2

s= ut+ 1/2 a t 2= 135.14 metres

Total distance= distance travelled in parts 1,2,3= 1260.14 m

= 1.26014 Km

= 0.783050996 mi

7)An electrically powered grindstone wheel rotates at 2,000 rpm for 50 s and the power is then switched off.

the wheel comes to rest 40.0 s later. Calculate: The angular deceleration in rad/s ^2 and rev/min/s.

Determine the total angular distance traveled over the 90 s time interval, expressed in both radians and revolutions?

1 rev=2pie rad; rev/rad=[.1592]; rad/rev=[2pie=6.283

change in angular velocity= 2000 rpm

= 12566 radians/minute

= 209.4333333 radians/second

change in time= 40 s

angular decelarion=change in angular velocity/change in time=

5.2358 rad/s2

= 50 rev/m/s = 0.833333333 rev/s^2

During first phase for 50 seconds

angular distance=w t= 1666.67 revolutions

During second phase for 40 seconds

angular distance=w t-1/2*angular deceleration*t^2

= 666.6666667 revolutions

Total= 2333.33 revolutions

= 14660.33 radians

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