Simplify each of the following expressions: `4s t\ (s-t)-6s^2(t-t^2)-3t^2(2s^2-s)+2s t(s-t)`

Find each of the following products: (-2x^2)xx(7a^2x^7)xx(6a^5x^5) (ii) (4s^2t)xx(3s^3t^3)xx(2s t^4)xx(-2)

Find the angle between each of the following pair of line: vecr=(2+s)hati+(s-1)hatj+(2-3s)hatk, vecr=(1-t)hati+(2t+3)hatj+hatk

The displacement s of an object is given as a function of time t by the following equation s=2t+5t^(2)+3t^(3) . Calculate the instantaneous velocity of the object at t = 1 s.

A particle moves along the X-axis as x=u(t-2 s)+a(t-2 s)^2 .

Determine the order and degree of each of the following differential equation. State also whether they are linear or non-linear: s^2(d^2t)/(d s^2)+s t(dt)/(d s)=s

The position of object moving along an x-axis is given by x=3t-4t^(2)+t^(3) , where x is in meters and t in seconds. Find the position of the object at the following values of t : (i) 2s, (ii) 4s, (iii) What is the object's displacement between t = 0 s and t = 4 s ? and (iv) What is its average vvelocity for the time interval from t = 2 s to t = 4 ?

Remove the brackets and simplify : 3(3s - 2t) - 4 (s+2t)

The position (in meters) of a particle moving on the x-axis is given by: x=2+9t +3t^(2) -t^(3) , where t is time in seconds . The distance travelled by the particle between t= 1s and t= 4s is m.

A one-dimensional force F varies with time according to the given graph. Calculate impulse of the force in following time intervals. (a) From t=0s to t=10s . From t=10 s to t=15s . (C) From t=0 s to t=15s .