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