Ask question

Ask question

All categories

3 years ago

12

An object starts from rest and has an acceleration given by a = 3.00 t^2 – 4.20 t. Determine how far the object is from its star

ting point at the end of 4.50s using calculus.

1 answer:

Korolek [52]3 years ago

7 0

Answer:

38.7 units

Explanation:

a = 3.00 t² – 4.20 t

Integrate to find velocity as a function of time.

v = ∫ a dt

v = ∫ (3.00 t² – 4.20 t) dt

v = 1.00 t³ – 2.10 t² + C

The object starts at rest, so at t = 0, v = 0.

0 = 1.00 (0)³ – 2.10 (0)² + C

0 = C

v = 1.00 t³ – 2.10 t²

Integrate to get position as a function of time.

x = ∫ v dt

x = ∫ (1.00 t³ – 2.10 t²) dt

x = 0.250 t⁴ – 0.700 t³ + C

Find the difference in positions between t = 4.50 and t = 0.

Δx = [0.250 (4.50)⁴ – 0.700 (4.50)³ + C] – [0.250 (0)⁴ – 0.700 (0)³ + C]

Δx = 0.250 (4.50)⁴ – 0.700 (4.50)³

Δx = 38.7

The object moves 38.7 units.

You might be interested in

Determine which heat transfers below are due to the process of conduction. I) You walk barefoot on the hot street and it burns y

Taya2010 [7]

Answer:

I) You walk barefoot on the hot street and it burns your toes.

II) When you get into a car with hot black leather in the middle of the summer and your skin starts to get burned.

Explanation:

In conduction mode of heat transfer we know that the energy is transferred from one system to other system due to direct contact of two bodies

Here due to this direct contact the energy is transferred via a given solid or liquid medium

In this type of heat transfer medium particles will remain in its own position only the energy is transferred.

So here we can say the correct answer will be

I) You walk barefoot on the hot street and it burns your toes.

II) When you get into a car with hot black leather in the middle of the summer and your skin starts to get burned.

3 0

4 years ago

A 0.100-kg stone rests on a frictionless, horizontal surface. A bullet of mass 6.00 g, travel- ing horizontally at 350 m>s, s

mariarad [96]

Answer:

Magnitude is 25.8 m/s and direction is $35.5^{o}$

Explanation:

From the law of conservation of linear momentum

$m_{b}v_{ib}+ m_{s}v_{is}= m_{b}v_{fb}+ m_{b}v_{fs}$ where $m_{b}$ and $m_{s}$ are masses of bullet and stones respectively, $v_{ib}$ and $v_{is}$ are the initial velocities of bullet and stone respectively, $v_{fb}$ and $v_{fs}$ are the final velocities of bullet and stone respectively

Substituting 6g=0.006 Kg for mass of bullet, 0.1Kg for mass of stone, 350 m/s for initial velocity of bullet and 250 m/s as final velocity for stone but initial velocity of stone is zero

$0.006 Kg *350 m/s (\hat i)+0.1 Kg*0=0.006 Kg* 250 m/s (\hat j)+0.1*v_{fs}$

$2.1 Kg.m/s(\hat i)=1.5 Kg.m/s(\hat j)+ 0.1*v_{fs}$

$0.1*v_{fs}=2.1 Kg.m/s(\hat i)- 1.5 Kg.m/s(\hat j)$

$v_{fs}=21 Kg.m/s(\hat i)- 15 Kg.m/s(\hat j)$

$|v_{fs}|=\sqrt {(v_{x}^{2}+v_{y}^{2})}$

Substituting 21 for $v_{x}$ and 15 for $v_{y}$

$|v_{fs}|=\sqrt {(21^{2}+15^{2})}=25.8 m/s$

To find direction

$tan\theta=\frac {v_{y}}{v_{x}}$

$\theta=tan^{-1}(\frac {15}{21})=35.5^{o}$

Therefore, magnitude is 25.8 m/s and direction is $35.5^{o}$

8 0

4 years ago

When a surface is illuminated with electromagnetic radiation of wavelength 480 nm, the maximum kinetic energy of the emitted ele

algol [13]

Answer:

Max kinetic energy for 340 nm wavelength will be $2.238\times 10^{-19}j$

Explanation:

In first case wavelength of electromagnetic radiation $\lambda =480nm=480\times 10^{-9}m$

Plank's constant $h=6.6\times 10^{-34}J-s$

Maximum kinetic energy = 0.54 eV

Energy is given by $E=\frac{hc}{\lambda }=\frac{6.6\times 10^{-34}\times 3\times 10^8}{480\times 10^{-9}}=4.125\times 10^{-19}J$

We know that energy is given

$E=K_{MAX}+\Phi$ , here $\Phi$ is work function

So $4.125\times 10^{-19}=0.54\times 10^{-19}+\Phi$

$\Phi =3.585\times 10^{-19}J$

Now wavelength of second radiation = 340 nm

So energy $E=\frac{hc}{\lambda }=\frac{6.6\times 10^{-34}\times 3\times 10^8}{340\times 10^{-9}}=5.823\times 10^{-19}J$

So $K_{MAX}=5.823\times 10^{-19}-3.585\times 10^{-19}=2.238\times 10^{-19}j$

6 0

4 years ago

Which workout schedule would be BEST suited for a weight-lifting workout that builds both strength and endurance

VLD [36.1K]

My workout schedule is day on - day off

This helps the body rest after the work out and let it gain/build muscle mass

Good luck

4 0

4 years ago

Read 2 more answers

2. Why are the health-related fitness components more

ser-zykov [4K]

Answer:

Health-related physical fitness is primarily associated with disease prevention and functional health.

Explanation:

This is ur answer actually I just took it from Go ogle

7 0

3 years ago