Mathematics In ...

where C is a constant, can be expressed as:

If the force on an object as a function of displacement is F(x) = 3x² + x, what is work as a function of displacement w(x) (W = ∫ (fdx). Assume W(0)=0 and force is in the direction of the object's motion.

The velocity of a rocket, in metres per second, t seconds after it was launched is modelled by v (t) = 2t. What is the total distance travelled by the rocket during the first four seconds of its launch?

The work done by gravity exerting an acceleration of -10 m/s² for a 10 kg block down 5 m from its original position with no initial velocity is:

Water flows into a container of 1000 L at a rate of (180+3t) gal/min for an hour, where t is measured in minutes. Find the amount of water that flows into the pool during the first 20 minutes.

If v(t)=3t-1 and x(2)=1, then the original position function is:

If charge flown through a wire is given by q=3sin(3t), then-current flown through the wire at t = π/9 seconds is: (i = dq/dt)

A weight hanging from a spring is stretched down 3 cm beyond its rest position and released at time t=0 to bob up and down. Its position at any later time t is s=3cos(t). Then its velocity at time t is (velocity = ds/dt)

The position of a particle is given by

Then, at t = 2, its velocity is :

The instantaneous velocity at t = π/2 of a particle whose positional equation is given by