Kinematics by integration and distance · Short practice

Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.

Recall

Kinematics through integration — objective 1

Maths4U Original · Short practice

A particle has velocity \(v(t)=\left(t - 4\right) \left(t - 1\right)\) m/s for \(0\le t\le 5\), with t measured in seconds.

Find the first rest time.

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

Fresh review variant

Kinematics through integration — objective 1

Maths4U Original · Short practice

A particle has velocity \(v(t)=\left(t - 6\right) \left(2 t - 4\right)\) m/s for \(0\le t\le 8\), with t measured in seconds.

Find the first rest time.

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

Method

Kinematics through integration — objective 2

Maths4U Original · Short practice

A particle has velocity \(v(t)=\left(t - 6\right) \left(2 t - 4\right)\) m/s for \(0\le t\le 8\), with t measured in seconds.

Find the second rest time.

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

Fresh review variant

Kinematics through integration — objective 2

Maths4U Original · Short practice

A particle has velocity \(v(t)=\left(t - 4\right) \left(3 t - 9\right)\) m/s for \(0\le t\le 7\), with t measured in seconds.

Find the second rest time.

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

Apply

Kinematics through integration — objective 3

Maths4U Original · Short practice

A particle has velocity \(v(t)=\left(t - 4\right) \left(3 t - 9\right)\) m/s for \(0\le t\le 7\), with t measured in seconds.

Find the net displacement over the complete interval.

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

Fresh review variant

Kinematics through integration — objective 3

Maths4U Original · Short practice

A particle has velocity \(v(t)=\left(t - 3\right) \left(t - 1\right)\) m/s for \(0\le t\le 4\), with t measured in seconds.

Find the net displacement over the complete interval.

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

Check understanding

Kinematics through integration — objective 4

Maths4U Original · Short practice

A particle has velocity \(v(t)=\left(t - 3\right) \left(t - 1\right)\) m/s for \(0\le t\le 4\), with t measured in seconds.

Find the total distance over the complete interval.

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

Fresh review variant

Kinematics through integration — objective 4

Maths4U Original · Short practice

A particle has velocity \(v(t)=\left(t - 5\right) \left(2 t - 4\right)\) m/s for \(0\le t\le 7\), with t measured in seconds.

Find the total distance over the complete interval.

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

Try written exam-style problems →