Question

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

Answer 1

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 $t$ seconds:

$y = 4.9t^2$

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.

$\text{Average Speed = }\dfrac{\text{Total Distance traveled}}{\text{Total Time Taken}}$

Let us find the distance traveled in 4 seconds by putting t = 4 in the equation $y = 4.9t^2$

$y = 4.9\times 4^2 = 78.4\ m$

Now, let us put the values in the formula:

$\text{Average Speed = }\dfrac{78.4}{4} = \bold{19.6\ m/s}$

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

$Speed = \dfrac{d}{dt}y = 4 \times 4.9 t^{2-1}\\\Rightarrow Speed = \dfrac{d}{dt}y = 4 \times 4.9 t$

Now, let us put t = 4 seconds

Speed = $4\times 4.9\times 4$ = 39.2 m/s

The answers are:

Average Speed

C.) 19.6 m/s

Instantaneous Speed

D.) 39.2 m/s