Question

The height of an object thrown upward from the surface of a planet is given by the function s(t) = -2t2 + 28t, where t is the time in seconds and s(t) is the height in meters. What is the speed of the object at time t = 4?

Answer 1

The speed of the object at time, t=4 is
`20ms^(-1)`

Explanation:

The speed is calculated using the formula;

`Speed=(Distance)/(Time\:taken)`

The distance covered by the object is given in terms of t, as

`s(t)=-2t^2+28t`

At time t=4, the distance covered by the object is;

`s(4)=-2(4)^2+28(4)`

`s(4)=80m`

The speed can now be calculated by substituting t=4 and distance 80 meters to obtain;

`Speed=(80)/(4) =20ms^(-1)`

Answer 2

12 m/sec.

Explanation:

The height of an object thrown upward from the surface of a planet is given by the function s(t) = - 2t² + 28t.

Here t = time

and s(t) = height in time t

Since the object has been thrown upwards under gravity so speed of ball will decrease with the time.

That means it we calculate rate of change in speed,
`((ds)/(dt))`

We can get the velocity at any moment of time.

So we will differentiate or find the derivative of the given expression.

s(t) = -2t² + 28t

`(d[s(t)])/(dt)=(d[-2t+28t^(2)] )/(dt)`

V(t) = (-4t +28 )

Now at t = 4 velocity will be

V (4) = -4 × 4 +28 = -16 +28 = 12 m/sec.

The speed of the object is 12 meter per second.