The position of the front bumper of a test car under microprocessor control is given by x(t) = 2.31 m + (4.90 m/s2)t2 - (0.100 m/s6)t6. (a) find its position at the instants when the car has zero veloc

The equation of the car is given by the equation,

                          x(t) = 2.31 + 4.90t² - 0.10t⁶

If we are going to differentiate the equation in terms of x, we get the value for velocity.

                  dx/dt = 9.8t - 0.6t⁵

Calculate for the value of t when dx/dt = 0.

                 dx/dt = 0 = (9.8 - 0.6t⁴)(t)

The values of t from the equation is approximately equal to 0 and 2. 

If we substitute these values to the equation for displacement,

(0)   , x = 2.31 + 4.90(0²) - 0.1(0⁶) = 2.31

(2)    , x = 2.31 + 4.90(2²) - 0.1(2⁶) = 15.51

Thus, the positions at the instants where velocity is zero are 2.31 and 15.51 meters. 

Jenny and fred both play a long note on their trombones. a stationary observer hears the sound increasing and decreasing repeatedly in loudness. which of these must be true? the sound waves from the two trombones have slightly different frequencies.the sound waves from the two trombones have the same frequency.the sound waves from the two trombones have slightly different amplitudes.the sound waves from the two trombones have the same wavelength.the sound waves from the two trombones have slightly different velocities.  lolthe answer is          the sound waves from the two trombones have slightly different frequencies.