3. A body of mass 5 kg is dropped from a height of 100ft with zero velocity. Assuming no air resistance, find an expression for the velocity at any time t.

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A: This is a linear differential equation which have to be solved using integrating factor

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A: Let N(t) denotes the number bacteria present at time t. Use the proportionality constant k, to get…

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A:

Q: The Ideal Gas Law is PV = mRT where P is the pressure, V is the volume, m is the constant mass, R is…

A:

Q: Suppose that a particle moves along a straight line with velocity v(t) = 12 4t, where 0 ≤ t ≤ 2 (in…

A: For the particle moving in a straight line  Displacement 12t-2t2 Total distance travelled is 16…

Q: The ideal gas law pV = 0.082T shows the relationship among volume V, pressure p, and the temperature…

A:

Q: Suppose that a particle moves along a straight line with velocity v(t) = 10 – 5t, where 0 <t < 0.5…

A:

Q: |21. If a ball is projected upward from the ground with initial velocity vo and resistance…

A: Resistance is proportional to v2 hence, resistance = -ρv2

Q: 2. A body moves along the straight path. If the given initial velocity is 2t2 – 4t + 5, what is the…

A: Given initial velocity is     vt = 2t2-4t+5As we know that velocity is rate of change of…

Q: Suppose that a particle moves along a straight line with velocity v(t) = 11 – 5t, where 0 <t 0.5 (-…

A: NOTE: Refresh your page if you can't see any equations. .

Q: Suppose the height of a spacecraft at time 1 is given by f () = 27 E1 for 0 <15 3. Find an…

A:

Q: e) What are the domain and the range for this situation?

A:

Q: A mass of 2.5 kg is suspended from a spring with a known spring constant of 10 N/m and allowed to…

A:

Q: Suppose the position function of a moving object is given by s (æ) = Væ. Then the average velocity…

A: Given that: To find:

Q: Suppose a particle’s position is given by f (t) = −2 / t, where t is measured in seconds and f (t)…

A: Given: ft=-2t

Q: Let a metallic rod 20 cm long be heated to a uniform temperature of 100° C. Suppose that at t = 0,…

A: Your answer is dependent on x, position from left end, and is the sum of infinity series.

Q: 1. If a stone is thrown vertically upward frosthe surface of the moon with a velocity of 10 meters…

A: Follow the procedure given below.

Q: What is the velocity and distance covered in 5 seconds when acceleration is 0.02s^(-7/8)) m/s²,…

A: Given:    a = 0.02s(-7/8)     t = 5 sec

Q: 1 If a spherical drop of liquid evaporates at a rate proportional to its area, if initially its…

A: Let the surface area be A So rate of evaporates is dA/dt, According to the question, dVdtαAdVdt=-kA…

Q: Suppose that a particle moves along a straight line with velocity v(t) = 12 – 3t, where 0 <t < 0.5…

A: Solution

Q: s) If the mass of an object is 2kg and its acceleration is find the variation constant, k, If the…

A:

Q: comparing the surface area of a sphere with its volume and assuming that air resistance is…

A: We will solve the following.

Q: The curved. surface of a rod of length (l) is against the flow of heat. If bot of ends of the rod…

A: Given heart equation is ∂2u∂x2=1c2∂u∂t Since c2=1 So heat equation will be ∂u∂t=∂2u∂x2…

Q: Suppose that a particle moves along a straight line with velocity v(t) = 15 – 1t, where 0 <t < 11.5…

A: Given : v(t) = 15 - t  0≤ t ≤ 11.5

Q: 9. The surface area of a cylinder is A = 2h+2². If the radius is measured to be 6 inches with a max…

A: Given, Surface area of cylinder, A=2πrh+2πr2 Given radius r=6in with maximum possible error dr =…

Q: Suppose that a particle moves along a straight line with velocity v(t) = 13 - 3t, where 0<t < 4 (in…

A:

Q: Suppose that a particle moves along a straight line with velocity v(t) = 7 - 3t, where 0 ≤ t ≤ 0.5…

A:

Q: Suppose that a particle moves along a straight line with velocity v(t) = 7 – 4t, where 0 <t < 1.5…

A:

Q: If a rock is thrown vertically upward from the surface ofMars with velocity 15 m/ s  , its height…

A: Given that a rock is thrown vertically upward from surface of Mars with velocity 15 m/s. Its height…

Q: 1. Suppose that the volume V of a certain cone can be expressed as V =nh, where h is the height of…

A: For the solution of the problem follow the next steps.

Q: Suppose A is directly proportional to t. Explain what happens to t when A is increased by 5%.

A:

Q: 4. The position of an object at time t is given by x = 34f - 8t + 2, where x is in feet and t is in…

A:

Q: Each side of an equilateral triangle measures 3cm, with a possible error of 0.1cm. Using…

A: Given

Q: Suppose that a particle moves along a straight line with velocity v(t) = 10 - 1t, where 0 <ts 3 (in…

A:

Q: Use Newton- Rophson Methad to find th Of the equalion in the range Solution ex t x- 10, ex + X -

A: If an equation is f(x)=0, then according to Newton Raphson method: Xn+1=Xn-f(Xn)f'(Xn)…

Q: The upward velocity of a rocket can be computed by the following formula: то v = u * In (- - gt то…

A: According to newtons raphson method  xn+1=xn-f(xn)f'(xn)   ...(1)   Secant method…

Q: Use differentials to estimate the maximum error in the volume of a rectangular box with square base…

A: Here we find the error in volume by using differential.

Q: If a ball is thrown vertically upward from the roof of 4848 foot building with a velocity of 6464…

A: s(t) = 48 + 64t - 16t2Hence, s’(t) = 64 – 32ts”(t) = - 32When s is maximum, s’(t) = 0; hence 64 –…

Q: If 6 J of work are needed to stretch a spring from 11 cm to 13 cm and 10 J are needed to stretch it…

A: Let the natural length = l cmSo, the work 6J  to stretch a spring from 11 cm to 13 cm can be written…

Q: Suppose a rubber ball, when dropped from a given height, returns to a fraction p of that height. In…

A:

Q: A particle that moves along a straight line has velocity v(t) = t?e meters per second after t…

A: The displacement -velocity -time equation is given by, dsdt=v(t) The displacement during the first t…

Q: An object moving in a straight line has an acceleration in m/s2 given by a = 18t + 4. Find its…

A:

Q: 5. Explain in words what the output of sinh (y) geometrically represents. ule

A:

Q: A pitcher of buttermilk initially at 27°C is to be cooled by settling in on a place where the…

A: At time t=0 minutes, temperature of buttermilk = 270C   At time t=20 minutes, temperature of…

Q: Suppose that a particle moves along a straight line with velocity v(t) = 13 - 5t, where 0 ≤ t ≤ 1…

A: Here the velocity function is v(t)=13-5t   , where 0≤t≤1 (in meter per second). We have to find the…

Q: Suppose that a turtle is moving along a straight line, and its displacement s(t) at any given time t…

A: Given data: The expression for the displacement is s(t)=(t-√(t2+3)+√3). The given interval is [a,…

Q: (a) Find the velocity of the particle at time t. s'(t) = (b) When is the velocity 0? (Use n as the…

A: Follow the procedure given below.

Q: Suppose that a particle moves along a straight line with velocity v(t) = 14 – 3t, where 0 <t< 2 (in…

A: Given, Velocity of the particle = v(t) = 14 - 3t  We have to find the displacement at time t = 2 So,…

Q: Suppose that a particle moves along a straight line with velocity v(t) = 9- 6t, where 0<t< 0.5 (in…

A: Given: v(t) = 9 - 6t, t = 0.5s