Answer:
Acceleration of the car at t = 5 secs is [tex]120m/s^{2}[/tex]
Explanation:
The position of the car as a function of time is represented as
[tex]x(t)=4t^{3}+t+3[/tex]
Now by definition of acceleration we have
[tex]a=\frac{d^{2}x(t)}{dt^{2}}=\frac{d}{dt}(\frac{dx(t)}{dt})[/tex]
Applying the value of x(t) we obtain acceleration as follows
[tex]a=\frac{d}{dt}(\frac{d}{dt}(4t^{3}+t+3))\\\\\therefore a=\frac{d}{dt}(12t^{2}+1)\\\\\therefore a=24t\\\\\therefore a|_{t=5}=24\times 5=120m/s^{2}[/tex]
