Atoy car of mass 6 kg, moving in a straight path, experiences a net force given by the function f = −3t. at time t = 0, the car has a velocity of 4 m/s in the positive direction and is located +8 m from the origin.
the car will come instantaneously to rest at time t equal to

The car will come instantaneously to rest at time t equal to 4 seconds.

Explanation:

"The acceleration varies linearly with time

As here the accelartion varies with respect to time so we can not simply apply Newtons Law"

Using the informations:

Area = F*t/2 = -3t²/2

I = Qf - Qi (Qf = 0, the velocity is zero)

So I = -Qi = -mv

I = -6*4 = -24

-24 = -3t²/2

t = 4s

t = 4 s

Explanation:

We all know that:

I = F*dt.

And the impulse is the variation of the linear momentum.( I = dP)

Now,

Area = F*t/2 = -3t²/2

I = Pf - Pi (Pf = 0, the velocity is zero)

So,

I = -Pi = -mv

I = -6*4 = -24

-24 = -3t²/2  

48 = 3t²

16 = t²

t = 4 s

∴ The car will come instantaneously to rest at time t equal to 4 s