What is the bicyclist’s velocity at t=10s?

What is the bicyclist's velocity at t=10s? Expres

a) What is the bicyclist’s velocity at t=10s?
Express your answer using two significant figures.

b) What is the bicyclist’s velocity at t=25s?
Express your answer using two significant figures.

c) What is the bicyclist’s velocity at t=35s?
Express your answer using two significant figures.



Answer

General guidance

Concepts and reason
The concept required to solve the problem is velocity from the position-time graph. Initially, find the position coordinates of the object at the time given from the graph. Substitute the values in the velocity equation and then calculate the velocity at the given time.

Fundamentals

The velocity of the object at any time is the slope of position versus time graph. From the position time graph, the velocity is given as, -x Here, х is the final position of the object at time , and is the initial position of the object at time .

Step-by-step

Step 1 of 6

(a) Use the graph to find the initial position at time and final position х at time . The slope is same at an interval. So, use the slope of that interval to solve for velocity at that point. |( 50 m)|(x, =100 m)4=20 s
Sx(m)
100
50
t (s)
40
10
30
0
20 Graph 1: Position vs Time graph of the object.

The position coordinate of the object initially and finally that is at the time respectively is the given by the point where graph intersect a straight line parallel to position axis.

Step 2 of 6

Use the velocity equation. -x Substitute 100 m for х, 20 s for , 50 m for , and for in the above equation and calculate velocity. 100 m-50 m
v=
20 s 0s
50
m/s
20
2.5 m/s

Part a

The bicyclist’s velocity at time t = 10 s is 2.5 m/s.


The velocity of the object at any time is the slope of position versus time graph. From the position time graph, the velocity is given as, -x Here, х is the final position of the object at time , and is the initial position of the object at time .

Step 3 of 6

(b) Use the graph to find the initial position at time and final position х at time . The slope is same at an interval. So, use the slope of that interval to solve for velocity at that point. 4 20 s430 s|(x, =100 m)|( =100 m)x(m)
100
50
t (s)
40
10
30
0
20 Graph 2: Position vs Time graph of the object.

The position coordinate of the object initially and finally that is at the time respectively is the given by the point where graph intersect a straight line parallel to position axis.

Step 4 of 6

Use the velocity equation. -x Substitute 100 m for х, 30 s for , 100 m for , and 20 s for in the above equation and calculate velocity. 100 m 100 m
v=
30 s-20 s
0
m/s
10
0 m/s

Part b

The bicyclist’s velocity at time t 25 s is 0 m/s.


The velocity of the object at any time is the slope of position versus time graph. From the position time graph, the velocity is given as, -x Here, х is the final position of the object at time , and is the initial position of the object at time .

Step 5 of 6

(c) Use the graph to find the initial position at time and final position х at time . The slope is same at an interval. So, use the slope of that interval to solve for velocity at that point. 4=30st, 40 s|( =100 m)(x0 m)x(m)
100
50
t (s)
40
10
30
0
20 Graph 3: Position vs Time graph of the object.

The position coordinate of the object initially and finally that is at the time respectively is the given by the point where graph intersect a straight line parallel to position axis.

Step 6 of 6

Use the velocity equation. -x Substitute 0 m for х, 40s for , 100 m for , and 30 s for in the above equation and calculate velocity. 0 m-100 m
V=
40 s-30 s
100 m/s
10
=-10 m/s

Part c

The bicyclist’s velocity at time t 35 s is -10 m/s.


The velocity of the object at any time is the slope of position versus time graph. From the position time graph, the velocity is given as, -x

Here, х is the final position of the object at time , and is the initial position of the object at time .

Answer

Part a

The bicyclist’s velocity at time t = 10 s is 2.5 m/s.

Part b

The bicyclist’s velocity at time t 25 s is 0 m/s.

Part c

The bicyclist’s velocity at time t 35 s is -10 m/s.

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