Kinematics by differentiation · Short practice

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Recall

Kinematics through differentiation — objective 1

Maths4U Original · Short practice

A particle moves along a straight line with position \(s(t)=t^{3} - 12 t^{2} + 45 t + 17\) metres, for \(\displaystyle t\ge 0\) seconds.

Find the initial velocity in m/s.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Kinematics through differentiation — objective 1

Maths4U Original · Short practice

A particle moves along a straight line with position \(\displaystyle s(t)=\frac{t^{3}}{3} - \frac{5 t^{2}}{2} + 4 t + 18\) metres, for \(\displaystyle t\ge 0\) seconds.

Find the initial velocity in m/s.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Method

Kinematics through differentiation — objective 2

Maths4U Original · Short practice

A particle moves along a straight line with position \(\displaystyle s(t)=\frac{t^{3}}{3} - \frac{5 t^{2}}{2} + 4 t + 18\) metres, for \(\displaystyle t\ge 0\) seconds.

Find the initial acceleration in \(\displaystyle \frac{m}{s^{2}}\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Kinematics through differentiation — objective 2

Maths4U Original · Short practice

A particle moves along a straight line with position \(\displaystyle s(t)=\frac{2 t^{3}}{3} - 8 t^{2} + 24 t + 19\) metres, for \(\displaystyle t\ge 0\) seconds.

Find the initial acceleration in \(\displaystyle \frac{m}{s^{2}}\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Apply

Kinematics through differentiation — objective 3

Maths4U Original · Short practice

A particle moves along a straight line with position \(\displaystyle s(t)=\frac{2 t^{3}}{3} - 8 t^{2} + 24 t + 19\) metres, for \(\displaystyle t\ge 0\) seconds.

Find the first positive time when the particle is at rest.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Kinematics through differentiation — objective 3

Maths4U Original · Short practice

A particle moves along a straight line with position \(\displaystyle s(t)=t^{3} - \frac{21 t^{2}}{2} + 36 t + 20\) metres, for \(\displaystyle t\ge 0\) seconds.

Find the first positive time when the particle is at rest.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Check understanding

Kinematics through differentiation — objective 4

Maths4U Original · Short practice

A particle moves along a straight line with position \(\displaystyle s(t)=t^{3} - \frac{21 t^{2}}{2} + 36 t + 20\) metres, for \(\displaystyle t\ge 0\) seconds.

Find the next time when the particle is at rest.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Kinematics through differentiation — objective 4

Maths4U Original · Short practice

A particle moves along a straight line with position \(\displaystyle s(t)=\frac{t^{3}}{3} - 2 t^{2} + 3 t + 21\) metres, for \(\displaystyle t\ge 0\) seconds.

Find the next time when the particle is at rest.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Try written exam-style problems →