Question

The velocity as a function of time for a car on an amusement park ride is given as v= at^2 +bt, with constants a = 2.0 m/s^3 and b = 1.0m/s^2. if the car starts at the origin, what is its position at t = 3.0s.

Answer 1

The position of the car at t=3.0s is 18m from the origin.

the starting point of a quantity at a certain time, let's say t = 0. This is referred to as receiving an "initial condition",

For a car on an amusement park ride, the velocity as a function of time is given by v=at² + bt with constants.

According to the equation above,

• A function of time's derivative is a constant.
• Time affects the velocity.

v = t² + 2t

Since v = dx/dt

dx/dt = t² + 2t

dx = t²dt + 2tdt

Integrating both sides [ integration{ a^nda } = a^(n+1) / (n+1) ]

So , int [ x⁰dx ] = int [ t²dt ] + 2 int [ t¹dt ] ,

Now,

x¹/1 = t³/3 + 2*( t²/2 )

x = t³/3 + t²

For t =  s,

x = 3³/3 + 3²

x= 27/3 + 9 = 18 m .

Learn more about velocity here:

brainly.com/question/19979064

#SPJ1