Question

The position (x) of a moving object depends on time as
x=t³-3t²+4t+2
Find its velocity at the instant when its acceleration is zero.
Options
1. 1
2. -1
3. 2
4. -2​

Answer 1

Answer:

v =$\frac{dx}{dt }$

v= $\frac{d}{dt} t^{3} - 3t^{2} + 4t +2$

v = $3t^{2} -6t + 4$

now  a = $\frac{dv}{dt }$

a= $\frac{d}{dt} 3t^{2} -6t +4$

a = 6t - 6

here a= 0

6t-6=0

6t = 6

t= 1 sec

substituting time in those equations

v = 3*1 - 6*1 + 4

v= 3 - 6 + 4

v= -3 + 4

v= 1m/s

............................................................................

a = 6*1 - 6

a = 6-6

a = $0 m/s^{2}$