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Salsk061 [2.6K]
3 years ago
8

A car starts from rest at a stop sign. It accelerates at 2.0 m/s2 for 6.2 seconds, coasts for 2.5 s , and then slows down at a r

ate of 1.5m/s2 for the next stop sign. How far apart are the stop signs
Physics
1 answer:
BigorU [14]3 years ago
8 0

Answer:

the distance between the stop signs is 120.7 m.

Explanation:

The car moved in three stages;

(1) It accelerates from rest at 2.0 m/s² for 6.2 seconds

(2) it moved at a constant speed for 2.5 s

(3) it finally decelerate at the rate of 1.5m/s²

(1) The distance moved by the car during the first stage;

s₁ = ut + ¹/₂at²

s₁ = 0 + ¹/₂ (2)(6.2)²

s₁ = 38.44 m

(2) The distance moved by the car during the second stage;

calculate the constant speed of the car,

v = u + at

v = 0 + 2 x 6.2

v = 12.4 m/s

The distance moved by the  car as it coasts for 2.5s: s₂ = vt

s₂ = 12.4 x 2.5

s₂ = 31 m

(3) The distance moved by the car during the third stage;

When the car stops, the final velocity is zero.

v² = u² + 2as₃

a = -1.5 m/s², since the car slowed down or decelerated.

0 = 12.4² + (2 x - 1.5)s₃

0 = 153.76 - 3s₃

3s₃ = 153.76

s₃ = 153.76 / 3

s₃ = 51.253 m

The total distance moved by the car from the start to stop = s₁ + s₂ + s₃

d = 38.44 m + 31 m + 51.253 m

d = 120.7 m

Therefore, the distance between the stop signs is 120.7 m.

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Answer:

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From the question we are told that  

  The displacement in the morning is  S_{morning} =  (2200 \m , east) + (4000\ m\ north) + (100 \ m ,\ vertical)

   The displacement in the afternoon is  S _{afternoon}= (1300\ m ,\ west) + (2500 \ m ,\ north) - (300\ m ,\ vertical)

Generally the direction west is negative , the direction east is positive

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    (2200 \m , east) +( - 1300\ m ,\ west) = 900 \ m \ east

     (4000\ m\ north)  + (2500 \ m ,\ north) = 6500  \ m ,\ north

     (100 \ m ,\ vertical) - (300\ m ,\ vertical) = -200 \ m

From the above calculation we see that at the end of the hiking the hiker (you) is  200 m below his/her(your) initial position

Generally from Pythagoras theorem , the resultant displacement in the north east direction is

      a  =  \sqrt{900^2 + 6500^2}

=>     a  = 6562.0 \  m

Generally from Pythagoras theorem , the resultant displacement in vertical direction (i.e the altitude change )

      b = \sqrt{6500^2 +(-200)^2  }

=>   b =6503.1 \  m

   

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