Given the acceleration function a = 2t2 + t - 4, the velocity v is found by integrating a with respect to t:

Morning Brian — let's get this done. To find the velocity v from the acceleration a, we integrate the acceleration function with respect to time t. Step 1: Set up the integral for velocity. Given the acceleration function a = 2t^2 + t - 4, the velocity v is found by integrating a with respect to t: v = a\,dt v = (2t^2 + t - 4)\,dt Step 2: Perform the integration. Integrate each term of the acceleration function: v = 2t^2+12+1 + t^1+11+1 - 4t + C v = (2)/(3)t^3 + (1)/(2)t^2 - 4t + C Here, C is the constant of integration. Step 3: Use the initial condition to find the constant C. The problem states that v=0 when t=0. Substitute these values into the velocity equation: 0 = (2)/(3)(0)^3 + (1)/(2)(0)^2 - 4(0) + C 0 = 0 + 0 - 0 + C C = 0 Step 4: Write the final expression for velocity. Substitute the value of C back into the velocity equation: v = (2)/(3)t^3 + (1)/(2)t^2 - 4t The velocity v is expressed in m/s. The velocity of the particle is: v = (2)/(3)t^3 + (1)/(2)t^2 - 4t m/s Send me the next one 📸