2 interactive labs · AS & A Level Mathematics 9709
Displacement, Velocity and Acceleration Graphs
4.2 Kinematics of motion in a straight line · Edit the v–t graph or give s as a polynomial in t: gradient and area link s, v and a. Predict, then compare displacement with distance.
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About this lab
Edit the v–t graph or give s as a polynomial in t: gradient and area link s, v and a. Predict, then compare displacement with distance.
You will be able to
State that the gradient of a displacement–time graph is velocity and the gradient of a velocity–time graph is acceleration, and read their signs as directions.
Calculate displacement as the signed area under a velocity–time graph and distance as the sum of the areas taken as positive, then find the average velocity and the average speed.
Determine, by differentiating and integrating a polynomial in t, the velocity, acceleration and displacement of a particle and the times when it is instantaneously at rest, including the constant of integration.
Explain why a particle that is instantaneously at rest may still be accelerating, and when a negative acceleration is making the particle speed up.
Constant Acceleration: Choosing the Equation
4.2 Kinematics of motion in a straight line · Give three of s, u, v, a, t and predict which equation to use, then solve with signs. Try vertical motion (g = 10) and two particles meeting.
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About this lab
Give three of s, u, v, a, t and predict which equation to use, then solve with signs. Try vertical motion (g = 10) and two particles meeting.
You will be able to
Determine which of s, u, v, a and t is neither given nor wanted, and choose the constant-acceleration equation that leaves it out.
Calculate the unknown by substituting signed values into the chosen equation, stating the positive direction, and reject an answer that needs a negative time.
Determine the time, the velocity or the displacement of a particle moving vertically with a = ∓10 m s⁻², and explain why both answers of a quadratic in t can be valid.
Form one equation for each of two particles moving with constant acceleration and equate their displacements to find when they meet.
