Question

A car moves along a straight track. The car’s position is given by the function 4t^3 + t + 3, where s is in metres and t is in seconds. Determine the acceleration at t = 5s.

Answer 1

Acceleration of the car at t = 5 secs is
`120m/s^(2)`

Step-by-step explanation:

The position of the car as a function of time is represented as

`x(t)=4t^(3)+t+3`

Now by definition of acceleration we have

`a=(d^(2)x(t))/(dt^(2))=(d)/(dt)((dx(t))/(dt))`

Applying the value of x(t) we obtain acceleration as follows

`a=(d)/(dt)((d)/(dt)(4t^(3)+t+3))\\\\\therefore a=(d)/(dt)(12t^(2)+1)\\\\\therefore a=24t\\\\\therefore a|_(t=5)=24* 5=120m/s^(2)`