A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.) f(t) = t3 − 8t2 + 23t (a) Find the velocity at time t. v(t) = ft/s (b) What is the velocity after 1 second? v(1) = ft/s

(a) Velocity =

(b) Velocity after 1 second is 10 ft/s

Explanation:

We know that if we differentiate distance with respect to time, we get velocity.

Thus we can use the same concept with an equation for distance, and solve the question as follows:

(a) We simply differentiate the following equation:

After differentiating, this becomes:

This is also the new equation for velocity.

So, we have: Velocity =

(b) At time = 1 s, we have the velocity (using our velocity equation from part 1):

So velocity after 1 second is 10 ft/s

answer: a ball

explanation: because it will bounce

heats surface water up