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

Average Speed

C.) 19.6 m/s

Instantaneous Speed

D.) 39.2 m/s

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 = }\frac{\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* 4^2 = 78.4\ m`

Now, let us put the values in the formula:

`\text{Average Speed = }(78.4)/(4) = \bold{19.6\ m/s}`

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

`Speed = (d)/(dt)y = 4 * 4.9 t^(2-1)\\\Rightarrow Speed = (d)/(dt)y = 4 * 4.9 t`

Now, let us put t = 4 seconds

Speed =
`4* 4.9* 4` = 39.2 m/s

The answers are:

Average Speed

C.) 19.6 m/s

Instantaneous Speed

D.) 39.2 m/s