Please show work The position of the front bumper of a test car undermicroproces

Question

Please show work
The position of the front bumper of a test car undermicroprocessor control is given by x(t) =2.21 m + (4.65m/s2)t2 - (0.100m/s6)t6. (a) Find its position at the instants when thecar has zero velocity.
first instant
x = 1 m
second instant
x = 2 m

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

Please show work
The position of the front bumper of a test car undermicroprocessor control is given by x(t) =2.21 m + (4.65m/s2)t2 - (0.100m/s6)t6. (a) Find its position at the instants when thecar has zero velocity.
first instant
x = 1 m
second instant
x = 2 m

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

Explanation / Answer

The position of the front bumper of a test car under microprocessorcontrol is given by x(t) = 2.21 m + (4.65m/s2)t2 - (0.100m/s6)t6. (a) Velocity is v = dx/dt = 0             0 + 2(4.65 m/s2)t - 6(0.100m/s6)t5 = 0 On solving this equations we get t = 0 and t = 1.98s Now position of the tester at t = 0s is x = 2.21m + 0 -0 =2.21m Position of the tester at t = 1.98s is    x =2.21m + (4.65)(1.98s)2 - (0.100)(1.98)6    = 5.39 m (b) Acceleration of the tester is a = dv / dt          = 9.3 -30(0.100)t4 At t = 0 the acceleration of the tester is a = 9.3m/s2 At t = 1.98 s the acceleration of the tester is                a = 9.3 - (30)(0.100)(1.98s)4                   = -55.4m/s2

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