Question

Determine the acceleration when t=1s if v=4t^2+2

Answer 1

acceleration=v/t
t=1
v=4t^2+2
=4×1^2+2
=4+2=6
a=v/t=6/1=6

Answer 2

Data:
Time = t = 1 s
Velocity = V = 4 t² + 2
Acceleration = ?
Solution:
As we know that, acceleration is defined as the rate of change of velocity of an object with respect to time taken.
Therefore,
Acceleration = Change of Velocity / Time taken
In terms of Calculus,
Acceleration = dv / dt   ....... (1)
Since, 
v = 4 t² + 2
dv / dt = d / dt (4 t² + 2)
dv / dt = (4) (2) t²⁻¹
dv / dt = 8 t
Acceleration = 8 t  (from equation (1) )
Given that t = 1 s
So,
Acceleration = 8 (1)
Acceleration = 8 m/s²
This is the required answer.
Hope it's helpful. Thanks.