Physics
Physics
3rd Edition
ISBN: 9781259233616
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 2, Problem 78P
To determine

Sketch the graph of the traveller and time taken for the trip.

Expert Solution & Answer
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Answer to Problem 78P

The graph of the traveller is drawn and the time taken for the trip is 68s.

Explanation of Solution

The figure below shows the velocity versus time graph of the traveller.

Physics, Chapter 2, Problem 78P

The total distance between the stations is 0.60km, the acceleration for the first level is 1.0m/s2, time taken is 10.0s, the final velocity is 0m/s and the acceleration for the third level is 2.0m/s2.

Write the expression to calculate the initial velocity.

u=at

Here, u is the velocity, a is the acceleration for the first level and t is the time taken.

Substitute 10.0s for t and 1.0m/s2 for a in the above equation to calculate v.

u=1.0m/s2(10.0s)=10m/s

Write the expression to calculate the distance travelled in first level.

x1=12at2

Here, x1 is the distance travelled in first level.

Substitute 10.0s for t and 1.0m/s2 for a in the above equation to calculate x1.

x1=12(1.0m/s2)(10.0s)2=50m

Write the expression to calculate the distance travelled in third level.

x3=v2u22a3

Here, x3 is the distance travelled in third level, v is the final speed and a3 is the acceleration in third level.

Substitute 0m/s for v, 10m/s for u and 2.0m/s2 for a3 in the above equation to calculate x3.

x3=(0m/s)2(10m/s)22(2.0m/s2)=100m2/s24m/s2=25m

Write the expression to calculate the time taken in third level.

t3=x3(u2)

Here, t3 is the time taken in third level.

Substitute 25m for x3 and 10m/s for u in the above equation to calculate t3.

t3=25m(10m/s2)=5.0s

Write the expression to calculate the distance covered in second level.

x2=sx1x3

Here, x2 is the distance covered in second level and s is the distance between station.

Substitute 25m for x3, 0.60km for s and 50m for x1 in the above equation to calculate x2.

x2=0.60km(1000m1km)50m25m=525m

Write the expression to calculate the time taken in second level.

t2=x2u

Here, t2 is the time taken in second level.

Substitute 525m for x2 and 10m/s for u in the above equation to calculate t2.

t2=525m10m/s=52.5s

Write the expression to calculate the total time taken for the trip.

ttot=t+t2+t3

Here, ttot is the total time taken for the trip.

Substitute 52.5s for t2, 5.0s for t3 and 10.0s for t in the above equation to calculate ttot.

ttot=10.0s+52.5s+5.0s=67.5s68s

Conclusion:

Therefore, the graph of the traveller is drawn and the time taken for the trip is 68s.

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Chapter 2 Solutions

Physics

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