Question

Determine the velocity v(t) and the position y(t) of a vehicle that starts from rest at position y(0) = 0 and is subjected to the following accelerations:

a(t) = 40t³ +30t² +20 +10 m/s².

Answer 1

The velocity function v(t) can be found by integrating the given acceleration function a(t). The position y(t) can be further obtained by integrating the resulting velocity function, starting with initial conditions of zero velocity and position.

Step-by-step explanation:

To determine the velocity v(t) of a vehicle we need to integrate the given acceleration function a(t) = 40t³ + 30t² + 20 + 10 m/s² over time. Since the vehicle starts from rest, we know that the initial velocity, v(0), is 0. Integrating the acceleration function will give us the velocity function.

To determine the position y(t), we integrate the velocity function over time. Given that the initial position y(0) is 0, we can directly integrate the velocity function to find the position function.

The steps for solving for both velocity and position involve definite integrals from the given acceleration function, assuming initial conditions of zero velocity and zero starting position.