EDEXCEL 4MA1 HIGHER TIER
Calculus in Kinematics - Progressive Assessment
Section 3.4: Differentiation Applied to Motion (s, v, a)
A particle moves so that its displacement, s metres, from a fixed point O after t seconds is given by s = 4t² + 3. Find an expression for the velocity, v m/s, of the particle.
A particle moves so that its displacement s metres from a fixed point is given by s = t² + t. Find the velocity of the particle when t = 3 seconds.
The velocity v m/s of a particle after t seconds is given by v = 10t - 2. Find an expression for the acceleration, a m/s², of the particle.
A particle moves so that its displacement s metres is given by s = t³ - 2t + 5. Find the displacement when t = 0.
The velocity of a particle is given by v = 2t - 8. At what time is the particle at rest?
A particle moves so that its displacement s metres from a fixed point O is given by s = t³ - 3t. The particle is at rest when v = 0. Find the values of t when the particle is at rest.
A particle moves so that s = t³ - 5t². Find the acceleration of the particle.
A particle moves so that s = 5t - t². Find the initial velocity (velocity at t = 0).
A particle moves so that s = 10t - t². Find the maximum displacement of the particle.
The velocity of a particle is given by v = t³ - 6t². Find the value of t when the acceleration is 0.
A particle moves so that its displacement s metres from a fixed point O is given by s = t³ - 6t² + 9t. Find the distance between the two points where the particle is at rest.
A particle moves so that s = t³ + 2. Show that the particle never returns to the origin (s ≠ 0 for t > 0).
A particle moves so that s = 2t³ - 9t² + 12t. Find the velocity when the acceleration is 5 m/s².
A particle moves so that its displacement from O is given by s = t³ - 4t. If the particle starts at a point 3 metres from O (not at O), does the formula for s change? Explain your reasoning.
A rocket is launched vertically. Its height h metres above the ground after t seconds is given by h = 20t - 5t². Find the maximum height reached by the rocket.
Edexcel 4MA1 Grade Boundaries (Indicative)
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