At t minutes past 2pm, the time needed to 3 pm is 3minutes less than `(t^(2))/(4)` find t.

The activity of a radioactive sample is measured as N_0 counts per minute at t=0 and N_0//e counts per minutes at t=5 minutes. The time (in minutes ) at which the activety reduces to half its value is :

A car starts from a point P at time t = 0 seconds and stops at point Q. The distance x, in metres, covered by it, in t seconds is given by x=t^(2) (2-(t)/(3)) Find the time taken by it to reach Q and also find distance between P and Q.

The distance S (in kms ) travelled by a particle in time t hours is given by S (t) =( t^(2)+3t)/( 2) The distance travelled in 3 hrs .

Find the tangent and normal to the following curves at the given points on the curve. x = cos t, y = 2 sin^(2) t " at" t= (pi)/(3)

In a newly developed city, it is estimated that the voting population (in thousands) will increase according to V(t) = 30 + 12t^(2)-t^(3), 0 le t le 8 where t is the time in years. Find the approximate change in voters for the time change from 4 to 4(1/6) year.