Calculus Question (Pls show steps)

Question

A car travels along a straight road for 30 seconds starting at time t = 0. Its acceleration in ft/sec2 is given by the linear graph below for the time interval [0, 30]. At t = 0, the velocity of the car is 0 and its position is 10. What is the velocity of the car when t = 6? You must show your work and include units in your answer.

Answer 1

The acceleration is a linear function at + k where a is the slope of this line over time t and k is just a fixed number constant.

(1/2)at^2 + kt + C is the velocity function by integral calculus

The initial velocity is zero, so C=0.

The velocity function is (1/2)at^2 + kt

Integrating again, the position function is:

(1/6)at^3 + (1/2)kt^2 + C

The initial position is 10, so C=10 when t=0

The position function is (1/6)at^3 + (1/2)kt^2 + 10

At t=6 the velocity is (1/2)a(6)^2 + 6k

= 18a + 6k

THis is the best we can do, since the original linear function was NOT given