Abody moves along a straight line, its distance from the origin at any instant being given by the equation x = 8t − 3t2, where x is in centimeters and t is in seconds.

(a) find the average velocity of the body in the interval from t = 0 to t = 1 sec, and in the interval from t = 0 to t = 4 sec.
(b) find the expression for the average velocity in the interval from t to t + δt.
(c) what is the limiting value of this expression as δt approaches zero?
(d) find the time or times at which the body is at rest.
(e) find the expression for the acceleration at any time.

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)

An object moves from the position +34m to the position -15m in 15 seconds. what is it's total displacement? what is it's average velocity?

A2k pendulum has a speed of 1 m/s at a height of 1/2 meter