Suppose that the position vector for a particle is given as a function of time by vector r(t) = x(t)i hat bold + y(t)j hat bold, with x(t) = at + b and y(t) = ct2 + d, where a = 2.00 m/s, b = 1.30 m, c = 0.134 m/s2, and d = 1.04 m.

(a) Calculate the average velocity during the time interval from t = 2.10 s to t = 4.15 s.
vector v = m/s
(b) Determine the velocity at t = 2.10 s.
vector v =
m/s
Determine the speed at t = 2.10 s.

Aroll in a paper machine is powered by a separately excited dc machine. operating point 1 (under load): the roll typically operates at 764 rpm and must provide 301 nm of torque to oppose the load of the paper. the armature voltage is 230v for this operating point operating point 2 (no load): when the load is removed the speed of the roll increases to 900 rpm (the field characteristics are unchanged) la ea dev m (a) calculate the maximum torque (units of nm) that the motor can supply with this applied voltage (b) calculate the value of the armature resistance, ra (in ohms) (c) at operating point 1 (loaded condition), the field current, i, and the total input power (armature field), are measured to be to be 10 a and 28,600 w respectively. use this information to calculate the value of the field resistance, rf (in ohms). (d) (d) at operating point 1 (loaded condition), calculate the motor efficiency. express your answer as a percent to at least 2 significant digits. (d) if the field voltage is reduced by 1/2, calculate the new stall torque (in nm) of the motor (f). if the field voltage is reduced by 1/2, calculate the new no-load speed (in rad/sec)

Agas expands from an initial volume of 0.040 m^3 and an initial pressure of 210 kpa to a final volume of 0.065 m^3 while its temperature is kept constant. how much work is done by the system?

Atomic nuclei of almost all elements consist of