Question

Derived the equation for velocity and acceleration given that position x = v⁰t + ½ at², where v⁰ and a are the initial velocity and constant acceleration, respectively. Find the position, velocity, and acceleration of the object at t=4.0s. Assume that v⁰= 4m/s and a=5m/s².

Answer 1

$v_0 = 4\frac{m}{s}$

$a = 5\frac{m}{s^2}$

$x(t) = v_0t+\frac{at^2}{2}$

$x(t) = 4t+\frac{5t^2}{2}$

$x(4)= 16 +\frac{5*16}{2}= 56m$

$v(t) = x'(t)= 4+5t$

$v(4) = 4 +5*4=24\frac{m}{s}$

$a(t) = v'(t) = 5$

$a(4) = 5\frac{m}{s^2}$

$\text{Answer: }x(4)= 56m;v(4) = 24\frac{m}{s};a(4) = 5\frac{m}{s^2}$