An object dropped from the top of a tall building falls y = 4.9t^2 meters in the first t seconds. What is the object’s average speed during the first 4 seconds?
A.) 4.9 m/s
B.) 9.8 m/s
C.) 19.6 m/s
D.) 39.2 m/s
E.) 78.4 m/s

What is the objects instantaneous speed at t=4 seconds?
A.) 4.9 m/s
B.) 9.8 m/s
C.) 19.6 m/s
D.) 39.2 m/s
E.) 78.4 m/s

Respuesta :

Answer:

Average Speed

C.) 19.6 m/s

Instantaneous Speed

D.) 39.2 m/s

Step-by-step explanation:

Given the function to represent the distance traveled by the object in [tex]t[/tex] seconds:

[tex]y = 4.9t^2[/tex]

To find:

Object's average speed during the first 4 seconds ?

Instantaneous speed at t = 4 seconds

Solution:

Average speed of a moving object is given by, Total Distance covered divided by Total time taken.

[tex]\text{Average Speed = }\dfrac{\text{Total Distance traveled}}{\text{Total Time Taken}}[/tex]

Let us find the distance traveled in 4 seconds by putting t = 4 in the equation [tex]y = 4.9t^2[/tex]

[tex]y = 4.9\times 4^2 = 78.4\ m[/tex]

Now, let us put the values in the formula:

[tex]\text{Average Speed = }\dfrac{78.4}{4} = \bold{19.6\ m/s}[/tex]

For instantaneous speed, we need to differentiate y w.r.to t:

[tex]Speed = \dfrac{d}{dt}y = 4 \times 4.9 t^{2-1}\\\Rightarrow Speed = \dfrac{d}{dt}y = 4 \times 4.9 t[/tex]

Now, let us put t = 4 seconds

Speed = [tex]4\times 4.9\times 4[/tex] = 39.2 m/s

The answers are:

Average Speed

C.) 19.6 m/s

Instantaneous Speed

D.) 39.2 m/s

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