Question

If the equation of an average velocity of a sport car was given by the equation V(t) = 3t^2 -6t +24. Determine its displacement after 3 seconds​

Answer 1

72

Step-by-step explanation:

The displacement of an object can be found from the velocity of the object by integrating the expression for the velocity.

In this problem, the velocity of the sport car is given by the expression

`v(t)=3t^2-6t+24`

In order to find the expression for the position of the car, we integrate this expression. We find:

`x(t)=\int v(t) dt=t^3-3t^2+24t+C`

where C is an arbitrary constant.

Here we want to find the displacement after 3 seconds. The position at t = 0 is

`x(0)=0^3-0+0+C=C`

While the position after t = 3 s is

`x(3)=3^3-3(3)^2+24(3)+C=72+C`

Therefore, the displacement of the car in 3 seconds is

`d=x(3)-x(0)=72+C-C=72`