Question

Amy purchased a brand-new mountain bike, which she's riding through
the winding trails. The bike's displacement is given by
s(t) = t3 - 2t2 + 3. What is the bike's acceleration after three minutes?

Answer 1

Answer:

The Acceleration of bike after 3 minutes of ride is  14 meter² per minutes

Step-by-step explanation:

Given as :

The displacement of bike is the function of time

i.e s(t) = t³ - 2 t² + 3  meters

The Time of bike acceleration = t = 3 minutes

Let The Acceleration of bike = a meter² per minutes

Now, According to question

∵ Acceleration is define as the rate of change of velocity

i.e acceleration = $\dfrac{\textrm velocity}{\textrm time}$

or, a =  $\dfrac{\textrm v}{\textrm t}$

And

Velocity is define as rate of change of displacement

i.e velocity =  $\dfrac{\textrm displacement}{\textrm time}$

Or, v =  $\dfrac{\textrm s}{\textrm t}$

Since here displacement is function of time

So , v = $\frac{\partial s(t)}{\partial t}$

Or, v =   $\frac{\partial (t³ - 2 t² + 3)}{\partial t}$

Or, v = 3 t² - 4 t + 3

So, velocity is the function of time = v = 3 t² - 4 t + 3   meter per minutes

Now, Again

Acceleration = a = $\frac{\partial v}{\partial t}$

Or, a = $\frac{\partial (3 t² - 4 t + 3)}{\partial t}$

Or, a = 6 t - 4

∴  Acceleration is the function of time = a = 6 t - 4

Now, Acceleration of bike after 3 minutes

So, at t = 3 min

i.e a = 6 t - 4

Or, a = 6 × 3 - 4

Or, a = 18 - 4

∴  a = 14 meter² per minutes

Hence, The Acceleration of bike after 3 minutes of ride is  14 meter² per minutes . Answer