Hello guys, I had really hard time figuring these questions out. I know it is a

Question

Hello guys,

I had really hard time figuring these questions out.  I know it is a lot, but I really did what I can.

Thanks in advanced

1- A speedboat moving at 35.0 m/s approaches a no-wake buoy marker 100 m ahead. The pilot slows the boat with a constant acceleration of -3.5 m/s2 by reducing the throttle.

(a) How long does it take the boat to reach the buoy? ( s )

(b) What is the velocity of the boat when it reaches the buoy? (m/s)

2- A particle moves along the x axis. Its position is given by the equation x = 2.1 + 2.9t ? 3.5t2with x in meters and t in seconds.

(a) Determine its position when it changes direction. (m )

(b) Determine its velocity when it returns to the position it had at t = 0? (Indicate the direction of the velocity with the sign of your answer.) (m/s)

3-A certain automobile manufacturer claims that its deluxe sports car will accelerate from rest to a speed of 44.5 m/s in 8.45 s.

(a) Determine the average acceleration of the car.   (      m/s2

(b) Assume that the car moves with constant acceleration. Find the distance the car travels in the first 8.45 s.  (m)

(c) What is the speed of the car 10.0 s after it begins its motion if it continues to move with the same acceleration? (m/s)

4-Kathy tests her new sports car by racing with Stan, an experienced racer. Both start from rest, but Kathy leaves the starting line 1.00 s after Stan does. Stan moves with a constant acceleration of 3.4 m/s2 while Kathy maintains an acceleration of 5.37 m/s2.

(a) Find the time at which Kathy overtakes Stan. ( s from the time Kathy started driving)

(b) Find the distance she travels before she catches him. ( m )

(c) Find the speeds of both cars at the instant she overtakes him.

Kathy  (m/s)

Stan (m/s)

5-A motorist drives along a straight road at a constant speed of 22.0 m/s. Just as she passes a parked motorcycle police officer, the officer starts to accelerate at 2.50 m/s2 to overtake her. Assume that the officer maintains this acceleration.

Explanation / Answer

1)

a)s=ut+0.5at^2

u=35

a=-3.5

s=100

100=35t+(0.5*-3.5*t^2)

t=3.453s

b) speed=35-3.5t=22.599=22.6

2)

x = 2.1 + 2.9t ? 3.5t2

v=dx/dt=2.9-7t (changes direction when v=0)

0=2.9-7t

t=0.4128s

a) x = 2.1 + 2.9t ? 3.5t2

x=2.7

b)x=2.1 at t=0

x=2.1=2.1+2.9t-3.5t^2

2.9t-3.5t^2=0

t=0.8286

v=2.9-7t=-2.9m/s

3)

a)accelleration=44.5/8.45=5.266

b)given in question

distance travelled =44.5m=(0.5*a*t^2)=(0.5*5.266*8.45^2)

c)speed at 10s= 5.266*10=52.66m/s

4)

a)distance travelled equal

0.5*5.37*t^2=0.5*(t+1)^2*3.4

(t+1)/t=1.2567

t=3.895s

b)distance=0.5*5.37*t^2=40.732m

c)kathy=5.37*3.895=20.916

stan=16.643=3.4*4.895

5)distances must be equal

22t=0.5*2.5*t^2

22t=1.25t^2

t=17.6s

b)sped=at=2.5*17.6=44

c)distance=387.2m=0.5*2.5*17.6^2

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