a roller coaster rider is travelling in a straight line changes from a speed of 4 m/s to 16 m/s in 3 s. Calculate the acceleration of the ride

Answer 1

The first thing you should start with is a diagram, and then write down your variables:

v_o = 4 m/s

v_f = 16 m/s

t = 3 s

Before you continue, ask yourself if the acceleration is going in the same direction as the velocity or the opposite direction of the velocity.

We have 3 main equations in kinematics that each require different parameters: v_o, v_f , d, and t, where d represents the change in distance. Since we're not given a specific direction of motion, I'm not going to say it's Δx or Δy, but it is the difference between the starting point and the ending point in a linear direction.

Since it's important to remember all three of these equations, I encourage students to write all three down at the top of your page:

Average Velocity: v_f = v_o + a•t

Distance without time: v_f² = v_o² + 2•a•d

Distance with time (no final velocity): d = vo•t + 1/2•a•t²

The only parameters we have are the initial and final velocity along with the time. Since we're looking for acceleration, we will use the Average velocity formula.

Before plugging in any numbers, you should algebraically solve for the variable you are looking for. In this case it's a.

v_f = v_o + a•t

v_f - v_o = a•t

(v_f - v_o = Δv)

Δv/t = a

Now you can plug the numbers into your calculator and solve.

Answer 2

Acceleration is a measure of how the velocity of an object changes over time. Since the roller coaster is traveling in a straight line, and we are given the intial and final speeds of the roller coaster over a certain duration of time, we will be calculating the average acceleration. This is given by

a_avg = Δv/Δt

where the change in speed is

Δv = v_f - v_i = 16 m/s - 4 m/s = 12 m/s

and the change in time is

Δt = 3 s.

Plugging these into our average acceleration expression, we get an average acceleration of

a_avg = (12 m/s)/(3 s) = 4 m/s².