Help with Calculus!

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 position of the car when t = 20? You must show your work answer to 3 decimal places. Include units in your answer.

Answer 1

Answer: find acceleration from your graph, then x = 10 + 450*a

Method:

1. Kinematic Equation x = x₀ + v_o• t + (1/2) • a • t²
2. Here, x₀ = 10ft, t = 30 sec, v_o= 0 ft/sec, a is obtained from the graph (it will be the slope of your velocity plot, rise/run type stuff)
3. Plugging in knowns, x = 10 + (1/2)a(30²) = 10 + 450a

Since your figure was not able to attach, please let me know if you need any further clarification