4. A body moves so that its distance, s metres, from the starting point is s 12+

Question

4. A body moves so that its distance, s metres, from the starting point is s 12+5t after seconds 5. A circular oil spill at sea is spreading such that its radius is increasing at 0.5 metre per minute. Find the 6. If V-4rx2 and 3r +x - 5, find the maximum value of V and the values of r and x that give this 7. What rectangle with perimeter of 12 m has the largest area? 8. A rectangular storage area is to be constructed along the sides of a tall building. A security fence is Calculate distance, speed and acceleration after 2 seconds rate of increase of the area of the oil spill when its radius is 20 m maximum value. required along the remaining 3 sides of the area. Find the maximum area that can be enclosed with 1000 m of fencing.

Explanation / Answer

4.

distance is given by:

s = 12 + 5t + t^3

at t = 2 sec

s = 12 + 5*2 + 2^3 = 12 + 10 + 8

s = 30 m

Now speed is given by:

v = ds/dt = d(12 + 5t + t^3)/dt

v = 0 + 5*1 + 3*t^2

v = 3t^2 + 5

at t = 2 sec

speed, v = 3*2^2 + 5 = 12 + 5 = 17 m/sec

acceleration is given by:

a = dv/dt = d(3t^2 + 5)/dt

a = 6*t + 0 = 6t

at t = 2 sec

a = 6*2 = 12 m/sec^2

5.

Area of circle is given by:

A = pi*r^2

rate of increase of the area will be

dA/dt = pi*2*r*dr/dt = 2*pi*r*dr/dt

given that we need dA/dt, when r = 20 m and dr/dt = 0.5 m/min

So,

dA/dt = 2*pi*20*0.5 = 62.83 m^2/min

Please Upvote.

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.