MathAmigo

Kinematics

Secondary 4 Additional Math practice

Start free

Kinematics practice questions

Secondary 4 topics from the Additional Mathematics 4049 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

Practise Kinematics free

What this topic covers

Worked examples

Example 1

A particle moves along a straight line such that its displacement, s metres, from a fixed point O at time t seconds is given by s=2t3−t2−4ts = 2t^3 - t^2 - 4t. Find the velocity when t=2t = 2.
Show the worked solution
  • v=dsdtv = \frac{ds}{dt}
  • =6t2−2t−4= 6t^2 - 2t - 4
  • When t=2:\text{When } t = 2:
  • v=6(2)2−2(2)−4v = 6(2)^2 - 2(2) - 4
  • =24−4−4= 24 - 4 - 4
  • =16 m/s= 16 \text{ m/s}

Answer: 1616

Example 2

A particle moves along a straight line such that its displacement, s metres, from a fixed point O at time t seconds is given by s=t3+5t2−ts = t^3 + 5t^2 - t. Find the acceleration when t=2t = 2.
Show the worked solution
  • v=dsdtv = \frac{ds}{dt}
  • =3t2+10t−1= 3t^2 + 10t - 1
  • a=dvdta = \frac{dv}{dt}
  • =6t+10= 6t + 10
  • When t=2:\text{When } t = 2:
  • a=6(2)+10a = 6(2) + 10
  • =22 m/s2= 22 \text{ m/s}^2

Answer: 2222

Example 3

A particle moves along a straight line with velocity v=3t2−8t+4v = 3t^2 - 8t + 4 m/s. When t=0t = 0, s=4s = 4. Find the displacement when t=1t = 1.
Show the worked solution
  • s=∫v dts = \int v \, dt
  • =∫(3t2−8t+4) dt= \int (3t^2 - 8t + 4) \, dt
  • =t3−4t2+4t+C= t^3 - 4t^2 + 4t + C
  • When t=0, s=4:C=4\text{When } t = 0, \, s = 4: \quad C = 4
  • s=t3−4t2+4t+4s = t^3 - 4t^2 + 4t + 4
  • When t=1:\text{When } t = 1:
  • s=(1)3−4(1)2+4(1)+4s = (1)^3 - 4(1)^2 + 4(1) + 4
  • =1−4+4+4= 1 - 4 + 4 + 4

Answer: 55

Questions parents ask

Is it really free?

The free plan is permanent and does not ask for a card. It has daily limits on the AI feedback, and the paid plans lift them.

Which syllabus does this follow?

Additional Mathematics (4049), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

Other Secondary 4 Additional Math topics