A car can accelerate at a rate of 0.5 meters per second squared if it is already moving forwards at an initial velocity of 6 meters per second.
1. Write a differential equation for velocity. Write an initial condition for the velocity.

2. Solve the initial value problem you wrote in (1) to find a formula for velocity.

3. Use the formula for the velocity you found in (2) to write an initial value problem for the car’s position. Assume that the car is initially at position 0.

4. Solve the initial value problem you wrote in (3) to find a formula for the position of the car.

5 How fast is the car going after 30 seconds?