Answer:
v(t)=3t²+3, and a(t)=6t
v(0)=3cm/sec, and a(0)=0cm/sec²
v(1)=6cm/sec, and a(1)=6cm/sec²
Explanation:
Find velocity and acceleration functions ( v(t) and a(t) )
(Relevant background: Let's say f(t) is a function of y with respect to x. Think of the derivative of this function, f'(t) , as representing the rate at which y changes with respect to x)
s(t) is a function of distance with respect to time. Therefore, s'(t) - the derivative of this - represents the rate at which distance changes with time, which is just the definition of velocity. So we can say velocity v(t) = s'(t).
s(t)=t³+3t+3
s'(t)=v(t)=3t²+3
Similarly, if v(t) is a function of speed with respect to time, then v'(t) represents the rate at which speed changes with time, which is acceleration. So we can say that acceleration a(t)=v'(t)=s''(t)
v(t)=3t²+3
v'(t)=a(t)=6t
Find velocity and acceleration at t=0 and t=1
t=0
v(t)=3t²+3
v(0)=3(0²)+3
v(0)=3 cm/sec
a(t)=6t
a(0)=6(0)
a(0)=0 cm/sec²
t=1
v(t)=3t²+3
v(1)=3(1²)+3
v(1)=3+3
v(t)=6 cm/sec
a(t)=6t
a(1)=6(1)
a(1)=6 cm/sec²
