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 5m. Also find its acceleration at t =2 second.

Answer 1

Answer on 39692, Physics, Mechanics | Kinematics | Dynamics

If we have the law for velocity, we have to integrate it with respect to $t$ to get the low motion, that is instantaneous position of the car as a function of time. So we have

$s(t)=\int v(t)dt=-6t^{2}+12t+C$

where $C$ is integration constant, which can be find from given condition $s(0)=5$. We see that

$s(0)=-6\cdot 0^{2}+12\cdot 0+C=5$

$C=5$

Hence, instantaneous position of the car as a function of time is

$s(t)=-6t^{2}+12t+5$

To find acceleration, we have to differentiate the velocity with respect to $t$

$a(t)=\frac{d}{dt}v(t)=-12$

Hence, acceleration and $t=2$ seconds is -12 m/$s^{2}$.