Impulse from force-time graph

2 The graph shows how a force, \(F\), varies with time during a period of 0.8 seconds.
\includegraphics[max width=\textwidth, alt={}, center]{18522f4c-4aa2-4ef5-898f-5ad2b06e287c-03_440_960_568_516} Find the magnitude of the impulse of \(F\) during the 0.8 seconds.
Circle your answer.
[0pt] [1 mark]
1.0 Ns
1.6 Ns
2.2 Ns
3.2 Ns Turn over for the next question

2 As a particle moves along a straight horizontal line, it is subjected to a force \(F\) newtons that acts in the direction of motion of the particle. At time \(t\) seconds, \(F = \frac { t } { 5 }\)
Calculate the magnitude of the impulse on the particle between \(t = 0\) and \(t = 3\)
Circle your answer.
[0pt] [1 mark]
\(0.3 \mathrm {~N} \mathrm {~s} \quad 0.6 \mathrm {~N} \mathrm {~s} \quad 0.9 \mathrm {~N} \mathrm {~s} \quad 1.8 \mathrm {~N} \mathrm {~s}\) A conical pendulum consists of a light string and a particle of mass \(m \mathrm {~kg}\) The conical pendulum completes horizontal circles with radius \(r\) metres and angular speed \(\omega\) radians per second. The string makes an angle \(\theta\) with the downward vertical. The tension in the string is \(T\) newtons. The conical pendulum and the forces acting on the particle are shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{86817115-46a1-4702-8a33-8f9b05d69bb9-03_616_593_689_703} Which one of the following statements is correct?
Tick ( ✓ ) one box.
\(T \cos \theta = m r \omega ^ { 2 }\)
\includegraphics[max width=\textwidth, alt={}, center]{86817115-46a1-4702-8a33-8f9b05d69bb9-03_108_108_1567_900}
\(T \sin \theta = m r \omega ^ { 2 }\)
\includegraphics[max width=\textwidth, alt={}, center]{86817115-46a1-4702-8a33-8f9b05d69bb9-03_109_108_1726_900}
\(T \cos \theta = \frac { m \omega ^ { 2 } } { r }\)
\includegraphics[max width=\textwidth, alt={}, center]{86817115-46a1-4702-8a33-8f9b05d69bb9-03_109_108_1886_900}
\(T \sin \theta = \frac { m \omega ^ { 2 } } { r }\) □

3 A body, \(Q\), of mass 2 kg moves in a straight line under the action of a single force which acts in the direction of motion of \(Q\). Initially the speed of \(Q\) is \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). At time \(t \mathrm {~s}\), the magnitude \(F N\) of the force is given by $$F = t ^ { 2 } + 3 \mathrm { e } ^ { t } , \quad 0 \leq t \leq 4 .$$

1. Calculate the impulse of the force over the time interval.
2. Hence find the speed of \(Q\) when \(t = 4\).