Question

Sam is observing the velocity of a car at different times. After three hours, the velocity of the car is 51 km/h. After five hours, the velocity of the car is 59 km/h. Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the car at different times. Show your work and define the variables used. (5 points) Part B: How can you graph the equation obtained in Part A for the first six hours?

Answer 1

Assuming that the car is travelling at constant acceleration, follows the equation: v = (v_in) + at where v = velocity v_in = initial velocity, (at t = 0) a = acceleration t = time Given the conditions, v = 51 at t = 3, and v = 59 at t = 5 Eqn 1: 51 = (v_in) + a(3) Eqn 2: 59 = (v_in) + a(5) Solving for v_in and a (using a calculator) v_in = 39 a = 4 therefore the equation for the motion of the car is: v = 39 + 4t This equation can be plotted using excel or wolframalpha.