Concept explainers
A particle starts from rest and accelerates as shown in Figure P2.13. Determine (a) the particle’s speed at t = 10.0 s and at t = 20.0 s, and (b) the distance traveled in the first 20.0 s.
(a)
The particle’s speed at
Answer to Problem 13P
The particle’s speed at
Explanation of Solution
Write the equation for the final velocity of a particle.
Here,
The area under acceleration versus time graph under specific time intervals gives the change in velocity of the particle during the time interval. Speed is the magnitude of velocity.
The sides of a unit rectangle in the graph are
The area under the graph in the interval
Since the particle starts from rest, its velocity at
Substitute
The area under the graph in the interval
Substitute
Conclusion:
Therefore, the particle’s speed at
(b)
The distance travelled in the first
Answer to Problem 13P
The distance travelled in the first
Explanation of Solution
The area under velocity versus time graph under specific time intervals gives the displacements during the time interval.
In part (a), it is found that the velocity at
The velocity versus time graph is shown below.
The area from
Write the equation for the area of a triangle.
Here,
In figure 1, the base of the triangle from
Substitute
Here,
The area from
Write the equation for the area of a rectangle.
Here,
In figure 1, the length of the rectangle from
Substitute
Here,
The area from
In figure 1, the base of the triangle from
Substitute
Here,
In figure 1, the length of the rectangle from
Substitute
Here,
Write the equation for total distance travelled.
Here,
Conclusion:
Substitute
Therefore, the distance travelled in the first
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Chapter 2 Solutions
Principles of Physics: A Calculus-Based Text
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