The following equations give the x component of the position for four objects as

Question

The following equations give the x component of the position for four objects as functions of time:
object 1: x(t)=a, where a = 5 m
object 2: x(t)=bt+c, where b = +4 m/s and c = -1 m
object 3: x(t)=et2+ft, where e = +5 m/s2and f= -9 m/s
object 4: x(t)=gt2+h, where g = -5 m/s2and h = +20 m .

1.

What is the earliest time when object 4 is at the origin? Time t can be negative.

Express your answer with the appropriate units.

2. What is that object's velocity 1 s after the instant you calculated in the previous part?

Explanation / Answer

x(t)=gt2+h

Put the value of x =0 in the object 4 equation then

0 = (-5)t2 + 20

5t2 = 20

t2 = 4

t = 2s

b)

Differentiating the object 4 equation then

V= 2gt + 0

V = 2 (-5)(1)

V = -10 m/s

10 m/s in the negative x direction.

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