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ScientistGrades 9–11⏱ 20 min

Motion in a straight line

Drive a car with a starting velocity and constant acceleration. Position, velocity and acceleration graphs move together, and the area under v–t is the distance.

Standards: HS-PS2-1HSF-IF.B.6

1Wonder

A driver sees a red light and brakes hard. How far does the car travel before it stops? Engineers use the same three graphs you are about to build to design safe roads.

2Explore

Motion graphs lab

This activity needs a bigger screen

Turn your phone sideways, or open this lesson on a tablet or computer. The explanation and quiz below work here.

0204060position x (m)velocity v (m/s)acceleration a (m/s²)0 s2 s4 s6 s8 st = 8 sv = v₀ + at= 2 + 1.5 × 8 = 14 m/sx = v₀t + ½at²= 64 marea = displacement = 64 mSillyChili
Try this
  • Set a = 0. What do the x–t and v–t graphs look like?
  • Now give the car a positive acceleration. Why does the x–t graph curve upward?
  • Set v₀ = 10 m/s and a = −2.5 m/s². When does the car stop? Then what happens?
  • Drag the time slider. Compare the shaded area under v–t with the position x.

3Explain

0xvaSillyChili
Step 1 of 5

Position, velocity, acceleration

Position x is where the car is. Velocity v is how fast its position changes, with a direction. Acceleration a is how fast the velocity changes.

Constant accelerationv=v0+a tx=x0+v0 t+12a t2\begin{aligned} v &= v_0 + a\,t \\ x &= x_0 + v_0\,t + \tfrac12 a\,t^2 \end{aligned}

Velocity is the slope of x–t, acceleration is the slope of v–t, and the area under v–t is the displacement.

4Practice

Question 1 of 5

A car starts at 4 m/s and accelerates at 2 m/s². What is its velocity after 3 s?

m/s

5Recap

  • Velocity is the slope of the x–t graph; acceleration is the slope of the v–t graph.
  • With constant a: v = v₀ + at and x = x₀ + v₀t + ½at².
  • The area under v–t is the displacement.
  • Negative acceleration with positive velocity means slowing down.