5. The position of a particle moving along the x-axis is given by x -30 t-30t,wh

Question

5. The position of a particle moving along the x-axis is given by x -30 t-30t,where x is in meters and t is in seconds. What is the position of the particle when it achieves its maximum speed in the positive x-direction? A) 42m B) 27 m C) 5.6m D) 9.8 m E) 3m 6. A bridge that was 6 m long has been washed out by the rain several days ago. How fast must a car be going to successfully jump the stream? Although the road is level both sides of the bridge, the road on the far side is 2.5 m lower than the road on this side. A) 12 m/s B) 36 m/s C) 12 m/s D) 7.5 m/s E) 8.4 m/s

Explanation / Answer

5.

x = 30 t2 - 30 t4

taking derivative both side relative to "t"

dx/dt = 60 t - 120 t3

v = 60 t - 120 t3

taking derivative both side relative to "t"

dv/dt = 60 - 360 t2

at maximum speed , dv/dt = 0

60 - 360 t2 = 0

t = 0.41 sec

Position is given as

x = 30 t2 - 30 t4 = 30 (0.41)2 - 30 (0.41)4 = 4.2 m

6.

vo = initial velocity = 28.3 m/s

= angle of launch = 30

consider the motion along the vertical direction or Y-direction

Voy = initial velocity In Y-direction = 0 m/s

a = acceleration = - 9.8

Y = displacement = - 2.5 m

t = time of travel

using the equation

Y = Voy t + (0.5) at2

- 2.5 = (0) t + (0.5) (- 9.8) t2

t = 0.71 sec

consider the motion along the horizontal direction or X-direction

Vox = initial velocity In X-direction = ?

a = acceleration = 0

X = displacement = 6 m

t = time of travel = 0.71 sec

using the equation

X = Vox t + (0.5) at2

6 = Vox (0.71)+ (0.5) (0)(0.71)2

Vox = 8.4 m/s

t = 2.88 sec

Related Questions

Navigate

• Browse (All)
• Browse 5
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.