the height of an object thrown on the surface of a certin planet is s(t)=80t-16t^2. what is the velocity? what is the acceleration? when is the velocity zero?

v(t) = s'(t) = 80-32t

a(t) = v'(t) = -32

when is velocity zero?
when is 80-32t = 0 ?
solve for t

To find the velocity and acceleration of the object, we need to differentiate the height function with respect to time.

The height function is given by s(t) = 80t - 16t^2.

1. Velocity (v):
To find the velocity, we differentiate the height function, s(t), with respect to time (t).

v(t) = ds(t)/dt

Differentiating s(t) = 80t - 16t^2:
v(t) = d/dt (80t - 16t^2)
= 80 - 32t

So, the velocity of the object is v(t) = 80 - 32t.

2. Acceleration (a):
To find the acceleration, we differentiate the velocity function, v(t), with respect to time (t).

a(t) = dv(t)/dt

Differentiating v(t) = 80 - 32t:
a(t) = d/dt (80 - 32t)
= -32

So, the acceleration of the object is a(t) = -32.

3. Velocity zero (t0):
To find when the velocity is zero, we set the velocity function v(t) = 80 - 32t equal to zero and solve for t.

80 - 32t = 0
32t = 80
t = 2.5

So, the velocity is zero when t = 2.5 seconds.

In summary:
- The velocity of the object is v(t) = 80 - 32t, where t is time.
- The acceleration of the object is a(t) = -32 (constant).
- The velocity is zero when t = 2.5 seconds.