Final answer:
To find the bus's velocity at time t2 = 2.05 s given its acceleration function ax(t)=αt, we integrate the acceleration, apply the initial condition to find the integration constant, and then evaluate the velocity at the desired time.
Step-by-step explanation:
The student's question involves calculating the velocity of a bus at a certain time given its acceleration function. Since acceleration is given as a function of time (ax(t) = αt), we can integrate this function with respect to time to find the velocity function, and then use the velocity at time t1 to solve for the constant of integration. Finally, we can evaluate the velocity at time t2.
Step-by-step Solution:
Integrate ax(t) = αt to get the velocity function: v(t) = ½ αt² + C, where C is the constant of integration.
Use the given velocity at t1 = 1.10 s to solve for C.
With C found, evaluate the velocity function at t2 = 2.05 s to find the velocity at that time.
Given Information:
α (alpha) = 1.10 m/s³
Velocity at t1 = 4.95 m/s
Substituting the given information into the integral, we find C and then the velocity at t2. This problem utilizes concepts of acceleration, integration, and kinematic equations and is a practical application of calculus in kinematics.