Graphs 9
3 marks · NormalA particle moves along a straight line and its displacement from a fixed point at time seconds is given by .
Explain how you would find the velocity and acceleration of the particle at . Write down the values.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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Velocity at t=2: -2 m/s; Acceleration is constant at 4 m/s^2
Also accept: Velocity: -2 m/s, acceleration: 4 m/s^2
Common mistakes: Substituting the value before differentiating; Forgetting to differentiate twice for acceleration
Show mark scheme and worked solution
Marking points
M1 · 1 mark · States or uses that velocity is the first derivative of displacement.
A1 · 1 mark · Finds correct velocity at as -2 m/s.
A2 · 1 mark · Correctly finds acceleration as 4 m/s^2.
Worked solution
Velocity is the first derivative of s: .
At , .
Acceleration is the derivative of velocity: .
So acceleration is 4 m/s^2 at all times.