Question

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

Answer 1

Answer:

(i) v = 44 m/s

(ii) a = 72 m/s^2

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:

$\frac{dx}{dt}=20+(6)(4)t^3=20+24t^3$

for t = 1 is:

$v(t=1)=\frac{dx}{dt}=20+24(1)^3=44m/s$

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

$\frac{dv}{dt}=24(3)t^2=72t^2$

for t = 1

$a(t=1)=\frac{dv}{dt}=72(1)^2=72m/s^2$