Question

The distance covered by a car at a time, t is given by x = 20t + 6t4, calculate

(i) the instantaneous velocity when t = 1

(ii) the instantaneous acceleration when t =1

Answer 1

(i) v = 44 m/s

(ii) a = 72 m/s^2

Step-by-step explanation:

You have the following equation for the potion of a car:

`x=20t+6t^4`

(i) The instantaneous velocity is the derivative of x in time:

`(dx)/(dt)=20+(6)(4)t^3=20+24t^3`

for t = 1 is:

`v(t=1)=(dx)/(dt)=20+24(1)^3=44m/s`

(ii) The instantaneous acceleration is the derivative of the velocity:

`(dv)/(dt)=24(3)t^2=72t^2`

for t = 1

`a(t=1)=(dv)/(dt)=72(1)^2=72m/s^2`