The position of the front bumper of a test car under microprocessorcontrol is gi

Question

The position of the front bumper of a test car under microprocessorcontrol is given by x(t) = 2.13 m + (4.60m/s2)t2 - (0.100m/s6)t6. (a) Find its position at the instants when thecar has zero velocity.
first instant
x =   ? m
second instant
x =   ? m

Find its acceleration at the instants when the car has zerovelocity.
first instant
  ? m/s2
second instant
   ? m/s2 (a) Find its position at the instants when thecar has zero velocity.
first instant
x =   ? m
second instant
x =   ? m

Find its acceleration at the instants when the car has zerovelocity.
first instant
  ? m/s2
second instant
   ? m/s2

Explanation / Answer

To find instant when car has zero velocity, take  dx/dt and set to zero, the solve for t: . like this...        dx/dt = 9.2 t   - 0.6t5 .                    0 = 9.2 t   - 0.6 t5 .                    0 = t ( 4.6 - 0.3 t4) . So the two instants are    t =0        and     t = 1.9788 seconds . So at the first instant     x = 2.13 m . And at the second    x = 2.13 + 4.60 * 1.97882   - 0.1 *1.97886=     32.36m . The acceleration function is    dv/dt =   9.2 - 3t4 . So the two accelerations are .    t =0          a = 9.2m/s2 . t = 1.9788       a = 9.2- 3 * 1.97884 =    -36.8m/s2 . t = 1.9788       a = 9.2- 3 * 1.97884 =    -36.8m/s2

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