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Edexcel A-Level Mathematics A2 M2.1 Kinematics of a Particle Moving in a Straight Line or Plane Questions

Practise kinematics for particles in lines and planes, linking suvat, projectiles, vectors, graphs, differentiation and integration with motion.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
A2

Exam points

  • use suvat or projectile components to find times, speeds and distances
  • differentiate displacement or velocity functions to find rest times and acceleration
  • interpret speed-time graphs and vector directions from calculated motion values

Covered syllabus points

M2.1.1 - Motion in a vertical plane with constant acceleration, eM2.1.2 - Simple cases of motion of a projectileM2.1.3 - Velocity and acceleration whenM2.1.4 - Differentiating and integrating vectors

Question 1

[Maximum number: 9]

A particle P moves on the x-axis.

At time t=0, P is instantaneously at rest at O.
At time t seconds, t>0, the x coordinate of P is given by

x=2t72−14t52+563t32x=2 t^{\frac{7}{2}}-14 t^{\frac{5}{2}}+\frac{56}{3} t^{\frac{3}{2}}

Find

Question (a)

(a)

the non-zero values of t for which P is at instantaneous rest

[ 3 ]

Question (b)

(b)

the total distance travelled by P in the interval 0 <=slant t <=slant 4

[ 3 ]

Question (c)

(c)

the acceleration of P when t=4

[ 3 ]

Question 2

[Maximum number: 7]

At time t seconds, t>0, a particle P is at the point with position vector r m, where

r=(t4−8t2)i+(6t2−2t32)j\mathbf{r}=\left(t^{4}-8 t^{2}\right) \mathbf{i}+\left(6 t^{2}-2 t^{\frac{3}{2}}\right) \mathbf{j}

Question (a)

(a)

Find the velocity of P when P is moving in a direction parallel to the vector j

[ 4 ]

Question (b)

(b)

Find the acceleration of P when t=4

[ 3 ]
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