Answer:
(i) v = 44 m/s
(ii) a = 72 m/s^2
Explanation:
You have the following equation for the potion of a car:
[tex]x=20t+6t^4[/tex]
(i) The instantaneous velocity is the derivative of x in time:
[tex]\frac{dx}{dt}=20+(6)(4)t^3=20+24t^3[/tex]
for t = 1 is:
[tex]v(t=1)=\frac{dx}{dt}=20+24(1)^3=44m/s[/tex]
(ii) The instantaneous acceleration is the derivative of the velocity:
[tex]\frac{dv}{dt}=24(3)t^2=72t^2[/tex]
for t = 1
[tex]a(t=1)=\frac{dv}{dt}=72(1)^2=72m/s^2[/tex]
