Question

The motion of a car along y-axis is given by v(t) = -12t +12 where velocity v is in m/s and time t in seconds. find the instantaneous position of the car as a function of time if at t= 0 it was at 5 m. Also find its acceleration at t=2 seconds.

Answer 1

Let instantaneous position of car be Y
$$\begin{gathered} Y=\int v\left(t\right)dt=\int \left(-12t+12\right)dt \\ =\left[-12\left(\frac{t^2}{2}\right)+12t\right]+C \\ =\left(-6t^2+12t\right)+C \\ Giventhatatt=0,Y=5m \\ 5m=-6{\left(0\right)}^2+12\left(0\right)+C \\ C=5m \\ Y=-6t^2+12t+5 \\ att=2 \\ Y=-6{\left(2\right)}^2+12\left(2\right)+5=5m \end{gathered}$$
a = dv/dt = -24 m/s^​2