vector R= (t^3-9t^2 + 24t + 10)jhat
The given expression represents a vector R in terms of the parameter t. The vector R is defined as R = (t^3 - 9t^2 + 24t + 10)jhat, where jhat represents the unit vector in the y-direction.
To understand more about this vector, we can break it down into its components. Since jhat is the unit vector in the y-direction, it means that the vector R has zero magnitude in the x-direction and its magnitude only depends on t in the y-direction.
The x-component of the vector R is 0, as there is no term multiplied by the ihat unit vector.
The y-component of the vector R is (t^3 - 9t^2 + 24t + 10) multiplied by jhat.
So, the vector R can be written as R = (0)ihat + (t^3 - 9t^2 + 24t + 10)jhat.
This representation of the vector R shows that its x-component is zero, and its y-component is determined by the expression (t^3 - 9t^2 + 24t + 10).
If you have a specific value for t, you can substitute it into the expression (t^3 - 9t^2 + 24t + 10) to find the corresponding y-component of the vector R.