Mathematics In Physics Test - 14

The instantaneous velocity (defined as v = ds/dt) at time t = π/2 of a particle, whose position equation is given as s(t)=12 tan (t/2 + π)m, is

If the acceleration a(t) = 4t+6, the velocity of a particle starting from rest is: (here, a = dv/dt)

A force of F(x) = 2x² + 3 N is applied to an object. How much work is done, in Joules, moving the object from x=1 to x=4 meters?

A car has a certain displacement between 0 seconds and 2 seconds. If we defined its velocity as v(t)=6t-5, then the displacement in meters is: (Here, v = ds/dt)

The relation between time t and distance x is t = ax² + bx, where a and b are constants, the acceleration is 

Given velocity v(t)= 5/2 t + 3. Assume s(t) is measured in meters and t is measured in seconds. If s(0)=0, the position s(4) at t=4s is: (Given, v = ds/dt)

The current through a wire depends on time as i =(2+3t) A. The charge that crosses through the wire in 10 seconds is: (Instantaneous current, i = dq/dt)

The area of a blot of ink, A, is growing such that after t seconds, A = 3t² + t/5 + 7m² . Then the rate of increase in the area at t= 5s will be :

A particle starts rotating from rest and its angular displacement is given by θ = t² / 40 + t/5. Then, the angular velocity (ω = dθ/dt) at the end of 10 s will be :