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.