To find the car's velocity after 3 seconds, we need to integrate the acceleration function from 0 to 3 seconds to obtain the change in velocity.
Given: Acceleration function: a(t) = 2t^2 + 2 Initial velocity: u = 10 m/s Time: t = 3 s
First, let's integrate the acceleration function to find the velocity function:
v(t) = ∫[a(t)] dt = ∫[(2t^2 + 2)] dt = (2/3) * t^3 + 2t + C
Since the initial velocity is 10 m/s, we can substitute the values into the velocity function and solve for the constant C:
10 = (2/3) * (0^3) + 2(0) + C 10 = 0 + 0 + C C = 10
Now we can plug the value of C back into the velocity function:
v(t) = (2/3) * t^3 + 2t + 10
To find the velocity after 3 seconds, substitute t = 3 into the velocity function:
v(3) = (2/3) * (3^3) + 2(3) + 10 = (2/3) * 27 + 6 + 10 = 18 + 6 + 10 = 34 m/s
Therefore, the car is going at a velocity of 34 m/s after 3 seconds.